The height of the apartment is 127.5 m.
What is the height of the apartment?
The height of the apartment is calculated by applying the following equation.
first equation for your throw; h = ¹/₂g(t +3.4)²
second equation for your friend's throw; h = vt + ¹/₂gt²
h = vt + ¹/₂gt²
h = 66.64t + ¹/₂gt²
now equate the two equations;
¹/₂g(t+3.4)² = 66.64t + ¹/₂gt²
¹/₂(9.8)(t² + 6.8t + 11.56) = 66.64t + ¹/₂(9.8)t²
4.9(t² + 6.8t + 11.56) = 66.64t + 4.9t²
4.9t² + 33.32t + 56.64 = 66.64t + 4.9t²
33.32t = 56.64
t = 1.7 seconds
The height of the apartment is calculated as;
h = ¹/₂g(t +3.4)²
h = ¹/₂(9.8)(1.7 +3.4)²
h = 127.5 m
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Select the correct answer from each drop-down menu.
Ellen is a prosecuting attorney. She ensures that only two parties have touched the physical evidence in her case. Who are these two parties?
Ellen ensures that only the
who initially collected the evidence, and the
✓ who
analyzed the evidence, are the only two people that touched the physical evidence, as indicated by their signatures on the seals of the
evidence bag and chain of custody document.
The selection of the correct word is as follows:
Ellen ensures that only the crime scene investigator initially collected the evidence, and the forensic technicians analyzed the evidence, are the only two people that touched the physical evidence, as indicated by their signatures on the seals of the evidence bag and chain of custody document.What is the role of forensic technicians?The role of forensic technicians is to visit crime scenes and gather, identify, classify, and analyze physical evidence related to criminal investigations. As a Forensic Science Technician, you will have required to perform tests on weapons or substances in order to determine their significance to the investigation.
They generally analyze crime scenes to determine what evidence should be collected and how. Along with this, they also take photographs of the crime scene and evidence and make sketches of the crime scene.
While the role of the crime scene investigator is to gather forensic evidence from crime scenes that will ultimately lead to the detection and prosecution of criminals. You'll process crime scenes using specialist techniques to visualize, capture and recover evidence.
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What is simple harmonic oscillation? Select all that apply.1. Simple harmonic oscillation occurs for objects whose motion can be defined by a sine or cosine curve. x(t)=x_0\cos(\omega t)x(t)=x 0 cos(ωt), for example2. Simple harmonic oscillation occurs for objects which experience a position (xx) dependent force (FF) of the form F=-CxF=−Cx, where C is some positive constant.3. Simple harmonic oscillation occurs when an object regularly returns to an equilibrium position.4. Simple harmonic oscillation only occurs for a mas-on-a-spring system.
a) [tex]x(t)=x_0\cos(\omega t)x(t)=x 0\ cos(\omega t),[/tex] for example
b) Simple harmonic oscillation occurs for objects which experience a position (xx) dependent force (FF) of the form F=-CxF=−Cx, where C is some positive constant.
What is Simple harmonic oscillation?Simple harmonic oscillation is a type of oscillatory motion in which an object oscillates back and forth around an equilibrium position. It is a special type of periodic motion in which the restoring force is always proportional to the displacement of the object from its equilibrium position, and acts in the direction opposite to that of the displacement. This type of motion is usually modeled by a mass-spring system.
a) Simple harmonic oscillation occurs for objects whose motion can be defined by a sine or cosine curve. x(t)=x_0\cos(\omega t)x(t)=x 0 cos(ωt), for example
b) Simple harmonic oscillation occurs for objects which experience a position (xx) dependent force (FF) of the form F=-CxF=−Cx, where C is some positive constant.
c) Simple harmonic oscillation occurs when an object regularly returns to an equilibrium position.
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Two gases—neon and air—are compressed in a closed system from P1 to P2 using a polytropic process with n = 1. 5. _____ requires lesser work to be compressed. The gas constants for neon and air are R = 0. 4119 and 0. 287 kJ/kg·K, respectively
In a closed system, two gases—neon and air—are compressed via a polytropic process with n = 1.5 from P1 to P2. Neon gas requires lesser work to be compressed.
In a polytropic process with n = 1.5, the equation that relates the initial pressure, P1, the final pressure, P2, and the specific heat ratio, n, is:
P1 x V1^n = P2 x V2^n
where V1 and V2 are the initial and final specific volumes of the gas, respectively.
Since the work done to compress a gas is given by the equation:
work = n x R x T x (V2^(1-n) - V1^(1-n))
We can find the work done to compress the two gases neon and air by substituting the values of the gas constant and the specific heat ratio into the equation:
Work to compress neon = 1.5 * 0.4119 kJ/kg·K * (V2^(1-1.5) - V1^(1-1.5))
Work to compress air = 1.5 * 0.287 kJ/kg·K * (V2^(1-1.5) - V1^(1-1.5))
Since the gas constant for neon is greater than the gas constant for air, it requires less work to compress neon than air. Therefore neon requires lesser work to be compressed.
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A company uses drones to fly food to people in regions that
have experienced natural disasters. The food is packed in
boxes that are attached to parachutes. How can the
company change the design of its parachute to reduce the
number of boxes that are damaged when they hit the
ground? (1 point)
The company can design a heavier parachute.
The company can design a smaller parachute.
The company can design a lighter parachute.
The company can design a parachute with more surface
area.
The parachute would be made to be heavier and more efficient. Option A
How can the parachute be redesigned?
We know that the way that the parachute functions would be related to the way that it is designed. We have to know that if the parachute is heavy, it is going to take a shorter time for the parachute to reach the ground because the air resistance would be overcome by the weight of the parachute.
For the redesign of the parachute. The best option is to ensure that the parachute us made in such a way that it is much heavy and able to travel through air easily.
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Answer: The company can design a parachute with more surface area.
Explanation: I just did the quick check and it was right!
two speakers play a 500 hz sound in phase. the speakers are arranged to face each other a what is the minimum distance you can move speaker a to achieve constructive interference along the x-axis? give a positive answer regardless of direction, in m.d are 6 m apart. how many points of constructive interference are there between the speakers?
As n is not an integer, so there will be no constructive interference between the speakers, if speaker A is moved by minimum distance.
What is interference?Interference is a phenomenon in which two waves combine by adding displacement together at every single point in space and time and to form a resultant wave of greater, lower, or same amplitude.
Wavelength of a 500 Hz sound wave is the speed of sound (about 343 m/s) divided by the frequency of the sound, which is 343/500 m = 0.686 m. Therefore, minimum distance you can move speaker A to achieve constructive interference along x-axis is 0.686/2 m = 0.343 m.
Given, distance between the speakers is 6m. Constructive interference will occur when path difference between two waves is equal to integer multiple of the wavelength. To achieve constructive interference, distance between the speakers + the distance moved by speaker A should be equal to n*wavelength where n is integer.
So, 6 + 0.343 = n* 0.686
n = (6+0.343)/0.686 = 8.8
As n is not an integer, so there will be no constructive interference between the speakers, if speaker A is moved by minimum distance.
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a diver moves horizontally from the underside of a bridge structure (position 1) to open water (position 2). ignoring effects like currents in the water, what pressure change will the diver sense between positions?
Option -C : Pressure stays the same because it is only a function of depth .
When the diver moves horizontally, the pressure is unaffected as pressure is function of depth only.
since,
p = denisty × gravity × depth
so only depends on depth.
The molecules and atoms that make up the many layers of the atmosphere are continually moving in arbitrary directions. Despite their small size, when they hit a surface, they apply pressure that humans perceive as a force. Since molecules can flow in any direction, they can even apply air pressure to an object as they collide from below. Air pressure can be applied in all directions in the atmosphere. An object or person suspended in a fluid and moving with it experiences static pressure. The pressure that develops when a flow is isentropically slowed to zero velocity is known as the stagnation pressure. The air pressure in various environments will vary, which will have an impact on how the vehicle operates. Air is thinner at higher altitudes,
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Question :
a diver moves horizontally from the underside of a bridge structure (position 1) to open water (position 2). ignoring effects like currents in the water, what pressure change will the diver sense between positions?
A . pressure increases from 1 to 2 because the bridge keeps the atmosphere from pushing down on the water at position 1.
B . pressure decreases from 1 to 2 because the weight of the bridge pushes down on the water at position 1.
C. Pressure stays the same because it is only a function of depth .
D. pressure may increase or decrease depending upon water properties like density.
a hypnotist's watch hanging from a chain swings back and forth every 0.43 s. what is the frequency (in hz) of its oscillation?
According to the problem the frequency of the oscillation (in hz) is 2.33 hz.
What is oscillation?Oscillation is a repetitive variation in the value of a physical quantity over time. It can involve a periodic change in the magnitude of a signal or the direction of a signal's movement. Examples include the swinging of a pendulum, the vibration of a tuning fork, the alternating current in an electrical circuit, and the periodic motion of a molecule. Oscillation is a key component of many natural phenomena, from ocean waves to the beating of a human heart. It is also a fundamental concept in physics, engineering, and mathematics. Oscillation is essential for the operation of numerous mechanical and electronic systems, from motors and generators to cell phones and radios.
The frequency of the oscillation (in hz) is 2.33 hz.
This is because frequency is equal to the inverse of the period (time) of the oscillation.
The period of the oscillation is 0.43 s, so the frequency is calculated by taking the inverse of 0.43 s,
which is 2.33 hz.
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Why is the gravitational
force that a friend
exerts on you less than
the gravitational force
exerted on you by
Earth?
As compared to Earth, humans have relatively low masses, which results in a very small and negligible gravitational force.
What does gravity mean?
The force of gravity, often known as gravitation, affects every material object in the universe. The force of gravity tends to draw any two objects or particles with nonzero mass toward one another. From subatomic particles to galaxy clusters, gravity affects things of all sizes.
The force of attraction between any two bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them, according to Newton's universal law of gravitation.
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a ball is tossed vertically upward with an initial speed of 25.5 m/s. how long does it take before the ball is back on the ground?
The ball will take 5.2 seconds to return back to its original position on the ground, if its initial speed is 25.5 m/sec.
The initial sped of the ball, u = 25.5 m/sec
Acceleration due to gravity of the earth, g = 9.81 m/s²
Let the time taken by the ball to reach highest point, = t
We know the final velocity of the ball after reaching the highest point is zero(0).
By the first equation of motion,
v = u + at
0 = 25.5 + (-9.81) × t
t = 25.5/9.81
t = 2.6 seconds
So the total time taken would be 2t = 2 × 2.6 = 5.2 seconds.
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approximately when does the full moon rise? select one: a. near sunrise b. near sunset c. near noon d. near midnight
approximately when does the full moon rise d. near midnight
When the full moon rises, where is the Sun?At Full Moon, the Moon is 180 degrees distant from the Sun and 12 hours behind it. As a result, the Moon rises as the Sun sets; it is high in the south around midnight and sets in the morning, at daybreak.
As a result, the moon advances eastward by around 12 degrees every day with regard to the sun (13 minus 1). This implies that the moon rises later and later each day, occasionally in the morning, occasionally in the afternoon, and occasionally at night.
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A ball is thrown with a initial upward velocity of 15m/s. What is the velocity after 1.5seconds?
The velocity after 1.5seconds is 0.3 m/s.
What is velocity?The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.
Initial upward velocity: u = 15 m/s.
Time interval: t = 1.5 second.
Acceleration due to gravity acting downward is = 9.78 m/s².
Let the final velocity is v.
Therefore,
v = u -gt
= (15 - 9.8 × 1.5) m/s
= 0.3 m/s.
So, the velocity after 1.5seconds is 0.3 m/s.
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a diver measures an ambient absolute pressure of 0.686 atm while diving in the ocean. what is the divers depth in feet?
2.250656 feet which are around 68.6 cm is the depth of the ocean at the place where the diver measured an absolute pressure is 0.686 atm.
As we know the pressure on the depth is directly proportional to that of depth in the meter as 1 atm has a meter of the column of water below which results in 1 atm of pressure.
And as given the pressure was 0.686 atm which shows the column below is just 0.686 mt or 68.6 cm. And to convert cm to feet we need to divide it by 30.48. So in this case
68.6/ 30.48 => 2.250656
So length in feet will be 2.250656 feet. We can say 2.25 feet after the round-off.
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the student explains how conduction is the charging by contact so the uncharged object takes
The student explains that conduction is the process of charging an object by touch. When two oppositely charged conductors make contact, this charge is divided between two conductors and is transferred to the uncharged conductor, which charges the conductor.
What is the conduction phenomenon explained?Conduction is one of the three main ways that heat energy is transferred.
When neighbouring atoms or molecules collide, heat energy is delivered by conduction.Conduction occurs more readily in both liquids and solids with smaller particle spacing than in gases with larger particle spacing.A rate of energy transfer by conduction is accelerated when there is a large temperature difference between the materials in contact.One class of solids that effectively transport heat is metals.Unsurprisingly, many pots and pans have insulated handles. A gaseous mixture of water and air is a poor conductor of thermal energy. They have the name "insulators."Consequently, When two oppositely charged conductors make contact, this charge is divided between two conductors and is transferred to the uncharged conductor, which charges the conductor.
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A) What happens when new evidence is found that contradicts part of a theory?(1 point)
The theory is discarded for a new one.
New pieces are added to the original ideas.
It gets ignored to maintain the original idea.
Science reevaluates the validity of the theory.
Science reevaluates the validity of the theory when new evidence is found that contradicts part of a theory.
When new evidence is found that contradicts part of a theory, scientists reevaluate the theory to see if it needs to be modified or if a new theory should be proposed. Scientists will look at the new evidence and try to reconcile it with the existing theory by adjusting or refining their understanding of the theory. If the new evidence cannot be reconciled with the existing theory, scientists may propose a new theory or modify the existing theory to better explain the new evidence. This process is an essential part of the scientific method and allows for theories to be continually refined and improved over time.
when new evidence is found that contradicts part of a theory, scientists engage in a process of critical evaluation and testing of the theory. This process can involve a variety of different steps and can lead to different outcomes depending on the nature of the new evidence and the existing theory.
One outcome could be that the new evidence is found to be inaccurate or unreliable, in which case the theory remains unchanged. Another outcome could be that the new evidence is found to be credible and significant, and so the theory is modified to account for the new information. This process of modifying a theory in light of new evidence is known as "theory modification" or "theoretical revision" and it is an important aspect of scientific inquiry.
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how far from the center of the earth would the net gravitational force of the earth and the moon on an object be zero?
At 346306 km from the center of the earth would the net gravitational force of the earth and the moon on an object be zero.
Let the mass of the earth and the mass of the moon be m1 and m2 respectively. The distance between the earth and the moon be D.
The formula for the gravitational force between two objects having masses m1 and m2 saperated by a distance D is given by the formula:
F = Gm1m2/r^2
The distance between the earth and the moon is also known:
D=384400km
Let at distance x from the earth the gravitational force between the earth and the sun is zero.
∴ Gm1/x^2=Gm2/(D-x)^2
⇒ (D-x)^2 /x^2 = m2/m1
Substituting the values we get of m1,m2 and D we get:
x=346306 km
Therefore, at 346306 km from the center of the earth would the net gravitational force of the earth and the moon on an object be zero.
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relief supplies are being dropped to flood victims from an airplane flying horizontally at a speed v. if the airplane is at an altitude of h above the ground, what distance d in front of the landing site should the supplies be dropped?
The distance d in front of the landing site should the supplies be dropped is v√(2h/g) meter. If the horizontal velocity of the airplane is v m/s and height of the plane from the ground is h.
Horizontal velocity of the airplane = v
height of the airplane = h
Initial velocity of the food, u = 0 m/s
From the second equation of motion,
S = ut +0.5gt²
h = 0.5gt²
t = √(2h/g)
It is time taken by the food to reach the ground. in this time the horizontal distance travelled by the food is, d = v × t
d = v × √(2h/g)
d = v√(2h/g)
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a smart phone charger delivers charge to the phone, in the form of electrons, at a rate of -0.75 c/s .how many electrons are delivered to the phone during 23 min of charging?
No. of electrons are delivered to the phone during 23 min of charging
6.46875 x 10^21
Charge is q = ne
where , e = - 1.6 x 10^-19
n = no.of electrons
The rate of accumulation of the electrons is ,q/t = Q
Q x t = -0.75 / 23 min = q
For time t = 23 min
1min = 60 sec
so time in sec, t = 23 x 60 = 1380 sec
therefore , Q x t = -0.75 x 1380
= -1035 c
No. of electrons = n = q/e
= -1035 / -1.6 x 10^-19
= 6.46875 x 10^21 electrons
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A student designs a gravity experiment. She will time how long it takes different objects to fall from her school’s roof to the ground. She will use three objects: a 2-foot-long board, a toy car, and a paper bag. What is wrong with her experiment’s design?(1 point)
The experiment’s design is not fair because the three objects do not have equal length to ensure they fall the same height.
What is a fair experiment?
A fair experiment or testis an investigation where one variable (the independent variable) is changed and all other conditions (controlled variables) are kept the same.
To fairly determine the time taken for different object to fall to the ground, the length of the objects should be the same, this ensures that the dependent variable is kept constant.
2-foot-long board is not the same length as a toy car, and a paper bag, so the experiment is not fair.
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recent significant breakthrough in space exploration
Recent significant breakthrough in the space exploration field is that webb telescope reveals the invisible universe.
With the help of various international space agencies, NASA notched steps forward in scientific endeavors. After decades of working, the James Webb Space Telescope finally began observing the universe in July. The world’s most powerful space telescope has turned its eyes on stars, planets, and galaxies by infrared light, which is invisible to the human eye.
The telescope has explored the unseen aspects of the universe and previously hidden figures, including the most distant galaxies ever observed. Webb has also shared new way of looking on some of astronomy’s favorite cosmic phenomenon and captured them in a new light, such as the Pillars of Creation.
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a 0.15 kg ball is thrown with a speed of 20.0 m/s. it is hit straight back at the pitcher with a final speed of 22.0 m/s. (a) what is the impulse delivered by the bat to the ball? (b) find the average force exerted by the bat on the ball if the two are in contact for 2.0 x 10-3 s
The average force exerted by the bat on the ball is 3200N and the impulse delivered by the bat on the ball is 6.30kgm/s
(a) The impulse delivered by the bat to the ball can be calculated using the equation Impulse = Change in Momentum.
Therefore, the impulse is equal to the difference between the final momentum and the initial momentum of the ball.
mΔv=0.15×42=6.3kgm/s
(b) The average force exerted by the bat on the ball can be calculated using the equation Force = Impulse/Time. Therefore, the average force is equal to the impulse divided by the time that the two are in contact. The time is 2 × [tex]10^{-3}[/tex]s. Therefore, the average force is equal to 150 N.
6.30/2×[tex]10^{-3}[/tex]= 3200N
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How much power is used if a force of 180N is used to push a box a distance if 60m in 20s
Answer:
Answer is in attached photo.
Explanation:
SolutionSolution is in attached photo, do take note there are 2 separate formulas to be used in this questions:
1) Work Done = Force x Distance
2) Power = [tex]\frac{Work \ Done}{Time}[/tex]
If a heat engine is operating between two temperatures (QH > Qc), what is the maximum efficiency attainable?
The maximum efficiency attainable for a heat engine operating between two temperatures (QH > Qc) is determined by the Carnot efficiency.
The Carnot efficiency represents the maximum theoretical efficiency that can be achieved by any heat engine operating between two temperatures. The formula for the Carnot efficiency is:
Efficiency = (Qc / QH) / 1.
where Qc is the engine's heat absorbed from the cold reservoir and QH is the engine's heat rejected by the hot reservoir.
It is important to note that for a heat engine to reach Carnot efficiency, it must operate in a reversible manner; in other words, it must be able to run in a cycle that can be reversed without any loss of energy. In practice, it is difficult to achieve Carnot efficiency in real-world heat engines due to the presence of friction and other inefficiencies.
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As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. There is no one around to help, so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. You pull up on the rope to lift the box. A) Once you have pulled hard enough to start the box moving upward, what is the magnitude F of the upward force you must apply to the rope to start raising the box with constant velocity? Express the magnitude of the force in terms of m, the mass of the box. F = 4. 9 m? b) Part B Consider lifting a box of mass m to a height h using two different methods: lifting the box directly or lifting the box using a pulley (as in the previous part). What is Wd/Wp, the ratio of the work done lifting the box directly to the work done lifting the box with a pulley? Express the ratio numerically.
Answer:
When you pull with a force upward so that the box is just about to rise, the sum of the two tensions (one from the ceiling and one from your hands pulling) equal the weight of the box. Thus C + H = W; where C is the ceiling rope tension and H is the hand rope tension. W = mg, the weight of the box.
Because there is no mechanical advantage in the single pulley, C = H, the two tensions are equal. So, we can write 2H = W = mg; and thus, H = W/2 = mg/2 when the box is just about to rise. To raise the box, you must have 2H>W; so that H > W/2 which means you need to yank upward on the rope in your hand with a force H (your F) just a bit over half the weight of the box.
Now here’s the tricky part. Once you’ve gotten the box to accelerate (start moving), you can relax the force H a bit so that it exactly equals H = W/2. Why? Because by keeping the net force f = ma = W – 2H = 0, acceleration settles in at a = 0 and the box is neither speeding up nor slowing down. It is then at constant velocity, which is what you specified.
Lesson here is that it takes a bit more force to get something to start moving, but once it starts to move we need to slack off a bit to maintain a constant velocity (too much force and it continues to speed up, too little and it slows down).
PS: Your question starts off with “Energy” then you talk and ask about force. They are not the same thing. I recommend you read up on the differences between energy and force. That will avoid a lot of confusion in future physics studies.
Explanation:
.
what is the relationship between the amount of energy required to remove thermal energy from a system, and the amount of thermal energy removed?
The amount of energy required to remove thermal energy is always greater or equal to the thermal energy removed, as per Second Law of Thermodynamics.
The Second Law of Thermodynamics is a fundamental principle of thermodynamics that states that the amount of energy required to remove a given amount of thermal energy from a system is greater than or equal to the amount of thermal energy removed.
This is also known as the Carnot's theorem and it is expressed mathematically as ΔQ < TΔS, where ΔQ is the heat absorbed or rejected, T is the temperature, and ΔS is the change in entropy. This means that it is impossible to completely convert heat into work, and some energy will always be lost as waste heat. This is why it is not possible to have a perpetual motion machine of the second kind.
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You are riding a bike with a bag in the front basket. A friend
on the sidewalk watches you ride by, heading south.
Which statement best describes how the bag's motion is
relative to the frame of reference - you and your friend?
O You observe the bag at rest, but your friend
observes it moving south.
You and your friend both observe the bag
moving to the south.
Your friend observes the bag accelerating
north, while you see it standing still.
O You and your friend observe the bag's velocity
decreasing.
Acceleration refers to an object's change in direction or speed or Velocity.
What is Acceleration?Forces have an impact on how things move. They have the power to initiate motion, as well as to stop, slow down, or alter the course of an item already in motion. We can contend that forces induce changes in velocity since they alter an object's velocity, which is the change in speed or direction.Remember that acceleration is a change in velocity. If the velocity is positive, a position is said to be increasing with time, and if the velocity is negative, a position is said to be decreasing with time.If the distance remains constant during that time, the velocity will remain zero. hence, the Acceleration Objects are said to be accelerating if they are altering their speed or direction.Forces affect how an object moves. They have the power to start anything moving, stop it mid-motion, slow it down, or change its course. Considering that forces alter an object's velocity, which is the change in speed or direction, we can claim that forces induce changes in velocity.As a result, when the object's velocity and acceleration are multiplied, the result is positive, the object moves faster, and when the result is negative, the object moves slower.To learn more about acceleration from the given link
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55. Cars A car moves 65 km due east then 45 km due
west. What is its total
displacement?
Answer:
A car moves 65 km due east and then 45 km due west. The car has traveled 65 km east and 45 km west, so it has covered a total distance of 65 + 45 = 110 km.
However, the displacement is the final point minus the initial point and not the total distance traveled. In this case, the car has traveled 65 km east and 45 km west, so it is back to its initial point. Therefore, its total displacement is 0 km.
Answer: The total displacement of the car is 20 km West.
Explanation:
This is because it moved 65 km East and then 45 km West, which effectively cancels out 65-45 = 20 km of the Eastward movement.
It does not matter how much distance the car covered in total, it only matters the net distance it moved in a certain direction.
what is the maximum distance we can shoot a dart, from ground level, provided our toy dart gun gives a maximum initial velocity of 2.78 m/s and air resistance is negligible?
If air resistance is negligible and our toy dart cannon generates a maximum initial velocity of 2.78 metres per second, we can shoot a dart up to a maximum distance of 0.74 metres from the ground.
Velocity is a time-dependent measure of how quickly an object's position changes in relation to a frame of reference. The velocity of an object indicates both its direction and speed of motion. Final velocity is a vector quantity that describes the speed and direction of a moving body after it has reached its maximum acceleration. The relationship between two points in physical space is given by the formula R = v2 sin2 theta/g.
R(max) equals v2/g if theta is 45 degrees.
R = 2.7^2 / 9.8 = .74 m
R = v^2 sin 2 theta / g
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(c16p12) suppose that the attraction between the moon and the earth were due to coulomb forces rather than gravitational force. what would be the magnitude of the charge required if equal but opposite charges resided on both earth and moon? mass of earth
The magnitude of the charge required if equal but opposite charges resided on both earth and moon is 1.037 × 10²⁰ Coulombs.
The magnitude of the charge required would be very large. Coulomb's law states that the force between two charges is given by
F = (k × q1 × q2) / r²
where k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between the charges.
To balance the gravitational force between the Earth and the Moon, we would need to set the Coulomb force equal to the gravitational force:
F_gravity = (G × m1 × m2) / r²
where G is the gravitational constant, m1 is the mass of the first object, m2 is the mass of the second object, and r is the distance between the objects.
By equating the two forces and solving for q1 and q2, we can find the magnitude of the charges required:
q1 × q2 = (m1 × m2 * G) / (k × r²)
q1 = q2 = √( (m1 × m2 × G) / (k × r²))
where mass of earth is 5.98 × 10²⁴ kg, mass of moon is 7.35 × 10²² kg, distance between earth and moon = 3.84 × 10⁸ m, and the Coulombs constant is 8.9875517873681764 × 10⁹ N×m²/C²
q1 = q2 = √( (5.98 × 10²⁴ kg × 7.35 × 10²² kg × 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻²) / (8.9875517873681764 × 10⁹ N×m²/C² × (3.84 × 10⁸ m)²)) = 1.037 × 10²⁰ Coulombs
Both the charges on Earth and Moon would be of 1.037 × 10²⁰ Coulombs
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Your question seems incomplete, but I assume the full question is:
"Suppose that the attraction between the moon and the earth was due to Coulomb forces rather than the gravitational force. What would be the magnitude of the charge required if equal but opposite charges resided on both earth and moon? Mass of earth = 5.98 × 10²⁴ kg; mass of moon = 7.35 × 10²² kg; earth-moon distance = 3.84 × 10⁸ m."
a muon is moving 11 m/s north when it experiences a constant acceleration of 8 m/s2 south. during this period it has a displacement of 444 m south. determine how long the muon was accelerating and what its velocity was when it finished accelerating.
The object was accelerating for 12 seconds and final velocity was 85m/s in south direction.
We can relate quantities like velocity, time, acceleration and displacement provided the acceleration remains constant. These relations are collectively known as the equation of motion. There are three equations of motion.
We know that from equations of motions : S = ut + 0.5 at^2
Where,
S = Distance or Displacement = 444 m (south)
u = initial speed = 11 m/s (north)
a = acceleration = 8 m/s^2 (south)
t =time
Now, Considering north to be positive direction, S = -444m and a = -8 m/s^2.
Putting these values in above equation we get:
8t^2 - 22t - 888 = 0
Solving this quadratic equation we get t = 12 seconds.
i.e. The object was accelerating for 12 seconds
Now, We also know that: v =u+ at
Where,
v = final velocity
u = initial velocity = 11m/s
a = acceleration = -8 m/s^2
t = time = 12 sec
Putting these values in above equation we get v = -85 m/s
Here, negative sign means that it is in s0uth direction.
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during a nascar race a car goes 76 m/s around a curved section of track that has a radius of 240 m. what is the car's acceleration?
The acceleration of the car is 24.07 m/s², if the velocity of the car is 76 m/s on a curve section of radius 240 m.
The speed of the car, v = 76 m/s
The radius of the curve, R = 240 m
On a curve there is a chance of overturning of the vehicle due to the lateral sloping of the curve(called super-elevation). This overturning force is balanced by the centrifugal force. Which is equal to, F = Mv²/R.
Where M is the mass of the vehicle and v, and R velocity and radius of the curve respectively.
So the acceleration would be, a = v²/R
a = 76²/240
a = 24.07 m/s²
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