Answer:
(a) [tex]2\vec A=12\hat i-4\hat j+6\hat k[/tex]
(b) [tex]\displaystyle \vec{U_A}=12/7\hat i-4/7\hat j+6/7\hat k[/tex]
(c) [tex]-4\vec{U_A}=-48/7\hat i+16/7\hat j-24/7\hat k[/tex]
Explanation:
Vectors
Given a vector
[tex]\vec A=6\hat i-2\hat j+3\hat k[/tex]
We must determine the following:
a) A vector in the same direction as A with double magnitude 2A.
If the vector goes in the same direction but has a different magnitude, we only need to multiply each component by a common factor, in this case, by 2. Thus, the required vector is:
[tex]2\vec A=12\hat i-4\hat j+6\hat k[/tex]
b) A unit vector in the same direction of A.
The unit vector needs to compute the magnitude of the vector:
[tex]\mid A\mid=\sqrt{6^2+2^2+3^2}[/tex]
[tex]\mid A\mid=\sqrt{36+4+9}=\sqrt{49}=7[/tex]
[tex]\mid A\mid=7[/tex]
The unit vector is:
[tex]\displaystyle \vec{U_A}=\frac{\vec A}{\mid \vec A\mid}[/tex]
[tex]\displaystyle \vec{U_A}=\frac{12\hat i-4\hat j+6\hat k}{7}[/tex]
[tex]\displaystyle \vec{U_A}=12/7\hat i-4/7\hat j+6/7\hat k[/tex]
c) A vector opposite to A with magnitude 4 m. We assume the original vector is also expressed in m.
The opposite vector to A is obtained simply by multiplying the unit vector by -1. To make its magnitude equal to 4, also multiply by 4. In all, we multiply the unit vector by -4:
[tex]-4\vec{U_A}=-4(12/7\hat i-4/7\hat j+6/7\hat k)[/tex]
[tex]-4\vec{U_A}=-48/7\hat i+16/7\hat j-24/7\hat k[/tex]
A "lovesick" individual wants to throw a bag of candy and love notes into the open window of their significant other’s bedroom 10.0 m above. Assuming it just reaches the window, they throw the gift at 60.0o to the ground: At what velocity should they throw the bag? How far from the house are they standing when they throw the bag? (Answer: A. 16.2m/s B. 11.5m)
Answer:
Explanation:
Let the velocity be v .
vertical component of the velocity = v sin 60 = √3 v /2
it reaches maximum height of 10 m .
v² = 2 gh
( √3 v/2 )² = 2 x 9.8 x 10
3 v² = 196 x 4
v² = 65.33 x 4
v = 16.2 m /s
Let time taken to reach height of 10 m
v = u - gt
v sin 60 = 9.8 t
16.2 x √3 /2 = 9.8 t
t = 1.43 s
horizontal distance covered = v cos 60 x t
16.2 x .5 x 1.43 = 11 .5 m
Suppose a signal from a vibrating motor is to be sampled discretely with a digital data acquisition system to determine the RPM of the motor. It is known that the maximum possible RPM is 1800. What is the minimum sampling frequency (in Hz) with which the signal can be sampled in order to measure the RPM of the motor
Answer:
f > 60 Hz
Explanation:
According to Nyquist's Sampling Theorem, to be fully reconstructed without any aliasing, the signal must be sampled at least more than twice during the period of the maximum frequency of the signal.In this case, the signal to be sampled has only one frequency.However, as we have the information in RPM, we need to convert this to cycles/sec (Hz) first, as follows:[tex]f = \frac{1800 rev}{min} * \frac{1 min}{60 sec} = 30 Hz[/tex]
Per Nyquist, fs > 2*30 Hz⇒ fs > 60 Hz
a box with a Constance velocity has a 5 N of force applied to it from all sides and direction. what will happen to the motion of the box as result?
A-the object will come to rest
b-the velocity of the object will remain the same
c- the velocity of the object will decrease
d- the velocity of the object will increase
Answer:
b-the velocity of the object will remain the same
Explanation:
Forces from opposite sides cancel each other, so there is no net force on the box that would affect its motion. The velocity of the box will remain unchanged.
__
(The box may be crushed, but it will continue in the same direction at the same speed.)
Answer:
b the velocity of the object will remain the same
Explanation:
use your brain:)
waht is science
wjwissbsskdldmndndnd
Answer:
the intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment.
Explanation:
Help me please :)
Answer the following questions to explain the relationship between electricity and magnetism.
• What are the critical components of an electromagnet and what purpose do they each serve?
• How can the strength of an electromagnet be changed?
• Why is an electromagnet considered a temporary magnet?
Answer the following questions about motors and generators.
• What components are needed for a generator to produce electric current?
• Describe motors and generators in terms of energy input and output.
HELP MEEEEEEEE
Decide if the following statements would be found in the Motor or Generator. Answers can be found at the end of the 3.07 Reading.
Statement Motor or Generator?
Answer:
R u from k12?? i am XD add me on discord my username is Hot Boy#1650
Explanation:
A car at the top of a ramp starts from rest and rolls to the bottom of the ramp, achieving a certain final speed. If you instead wanted the car to achieve twice as much speed at the bottom of the ramp, how high should the ramp be compared to the first case
Answer:
It must be 4 times high.
Explanation:
Assuming that the car can be treated as a point mass, and that the ramp is frictionless, the total mechanical energy must be conserved.This means, that at any time, the following must be true:ΔK (change in kinetic energy) = ΔU (change in gravitational potential energy)⇒ [tex]m*g*h = \frac{1}{2} * m*v^{2}[/tex]
Let's call v₁, to the final speed of the car, and h₁ to the height of the ramp.So, at the bottom of the ramp, all the gravitational potential energy
must be equal to the kinetic energy of the car (Defining the bottom of
the ramp as our zero reference for the gravitational potential energy):
[tex]m*g*h_{1} = \frac{1}{2} * m*v_{1} ^{2}[/tex] (1)
Now, let's do v₂ = 2* v₁Replacing in (1) we get:[tex]m*g*h_{2} = \frac{1}{2} * m*(2*v_{1}) ^{2}[/tex] (2)
Dividing (2) by (1), and rearranging terms, we get:h₂ = 4* h₁A recipe gives the instructions below
After browning the meat pour off fat from the pan to further reduce fat use a strainer.
what type lf separation methods are described in the recipe
A decantation and screening
B distillation and screening
C decantation and centrifugation
D distillation and filtration
Answer:
A. decantation and screening
Explanation:
Decantation is the one of the process of separating the mixture. In this process the precipitated liquid is separated from the solid. According to the given instruction for the recipe, the fat which is in liquid state is separated from meat. In the process of screening, more liquid is separated by placing the mixture on the screen. Here, the gravity plays an important role for the process of separation.
Answer:
a
Explanation:
block of mass m sits at rest on a rough inclined ramp that makes an angle with the horizontal. What must be true about normal force F on the block due to the ramp
Answer:
Explanation:
For a body on a ramp with mass m, the forces acting on the body along the vertical component are the weight and the normal reaction.
The weight of the body acts in the negative y direction while the normal reaction acts in the positive y direction
Taking the sum of forces along the y component
Sum Fy = -W+R = ma
Since acceleration is zero
-W+R = m(0)
-W+R = 0
-W = -R
W = R
Hence the Normal reaction force acting on the on the body is equal to normal force
3 For this force system the equivalent system at P is ___________ A FRP 40 lb along x dir and MRP 60 ft lbB FRP 0 lb and MRP 30 ft lbC FRP 30 lb along y dir and MRP 30 ft lbS FRP 40 lb along x dir and MRP 30 ft lb
This question is incomplete, the complete question is;
For this force system the equivalent system at P is ___________
A) FRP = 40 lb (along +x-dir.) and MRP = +60 ft.lb
B) FRP = 0 lb and MRP = +30 ft.lb
C) FRP 30 lb (along +y-dir.) and MRP = -30 ft.lb
D) FRP 40 lb (along +x-dir.) and MRP = +30 ft.lb
Answer:
D) FRP 40 lb (along +x-dir.) and MRP = +30 ft.lb
Explanation:
From the figure in the image i uploaded along this answer;
FRP = ( 40 lb i + 30 lb j ) + [30 lb (-j)]
Where i and j are the unit vectors along X & Y axis respectively.
So, FRP = 40 lb i
that is, FRP = 40 lb along +X direction
MRP = [ 30 lb x ( 1 ' + 1' ) ] +( -30 lb x 1 ' )
= (30 lb x 2 ' )- 30 lb ft
= 60 lb ft - 30 lb ft
= 30 lb ft
Therefore option(D) is correct
BRAINLIEST. Agraph is probelow. The graph shows the speed of a car traveling east over a 12 second period. Based on the information in the graph, it can be
that in the first second
Answer:speeding up constantly
Explanation:
The graph between the time and the speed of the car shows that the speed is increasing constantly, so, option C is correct.
What is speed?A moving object's rate of change in distance traveled is measured as speed. Speed is a scalar, which implies it is a measurement with a magnitude but no direction.
A thing that moves quickly and with high speed, covering a lot of ground in a short time. On the other hand, a slow-moving object traveling at a low speed covers a comparatively small distance in the same amount of time. An object with zero speed does not move at all.
Given:
The graph shows the speed of a car traveling east over a 12-second period,
As you can see from the graph, at time t = 0 sec the speed is 10 m/s,
At t = 3 sec, the speed = 15.3 m/s
At t = 6 sec, the speed = 20.3 m/s
Thus, speed is increasing constantly.
To know more about Speed:
https://brainly.com/question/13074982
#SPJ2
Please help
A student plans an investigation to determine the refractive index of glass. The student uses this equipments.
- a ray box
- a rectangular glass block
- a protractor
- a pencil
Describe how the student collect her data.
The Intensity level of a loud saw is 100 db at a distance of 5m. At what distance would the level be 80 db
Answer:
50 m
Explanation:
The relationship between the intensity of sound in dB and distance is given by the formula:
[tex]B_2=B_1+20log(\frac{R_1}{R_2} )\\\\Where \ B_2\ is \ the\ sound\ intensity\ at\ distance\ R_2\ and\\B_1\ is \ the\ sound\ intensity\ at\ distance\ R_1\ \\\\Given\ that: B_1=100\ dB, R_1=5\ m, B_2=80\ dB\\\\B_2=B_1+20log(\frac{R_1}{R_2} )\\\\80=100+20log(\frac{5}{R_2} )\\\\-20=20log(\frac{5}{R_2} )\\\\log(\frac{5}{R_2} )=-1\\\\\frac{5}{R_2}=10^{-1}\\\\\frac{5}{R_2}=0.1\\\\R_2=5/0.1=50\ m[/tex]
Calculate the effective charges on the H and F atoms of the HF molecule in units of the electronic charge, e.
Answer:
Explanation:
Hydrogen fluoride (HF) is an ionic/electrovalent compound that dissociates into ions when dissolved in water. It's dissociation is as seen below
HF ⇄ H⁺ + F⁻
There is a transfer of electron from the hydrogen atom which produces the hydrogen ion (H⁺), while the fluorine atom receives the donated ion to become negatively charged (F⁻). The amount of charge in one electron is generally given as 1.602 × 10⁻¹⁹ coloumbs.
The required value of effective charge on HF molecule, due to H and F is 1.602 × 10⁻¹⁹ Coulombs.
The given problem is based on the concept of effective charges. The net positive charge carried out by the electrons of atomic species, after forming a polyelectronic atom is known as Effective charge.
As per the given problem, the Hydrogen fluoride (HF) is an ionic/electrovalent compound that dissociates into ions when dissolved in water. It's dissociation is given as,
HF ⇄ H⁺ + F⁻
There is a transfer of electron from the hydrogen atom which produces the hydrogen ion (H⁺), while the fluorine atom receives the donated ion to become negatively charged (F⁻). The amount of charge in one electron is generally given as 1.602 × 10⁻¹⁹ Coulombs.
Thus, we can conclude that the required value of effective charge on HF molecule, due to H and F is 1.602 × 10⁻¹⁹ Coulombs.
Learn more about the effective charge here:
https://brainly.com/question/25002720
Why is our (a person's) gravitational pull NOT as strong as the Earth's gravitational pull
on us?
Gravity doesn't act on us
The Earth is closer to us than the Moon
Our mass doesn't change so the pull is really the same
We are much smaller than the Earth.
Answer:With gravity, two things with mass will want to move toward each other. However, we humans don't feel our gravity pulling on another person because it's not very big, but we do all feel the pull of Earth's gravity all the time - we're not all floating in the air, because that would be happening without Earth's gravity!
Explanation:
A chef places an open sack of flour on a kitchen scale. The scale reading of
40 N indicates that the scale is exerting an upward force of 40 N on the sack. The magnitude of this force equals the magnitude of the force of Earth’s gravitational attraction on the sack. The chef then exerts an upward force of
10 N on the bag and the scale reading falls to 30 N.Draw a free-body diagram of the latter situation.
Answer:
Explanation:
Given
Initial reading on scale =40 N
So, we can conclude that weight of the sack is 40 N
After this a 10 N force is applied upward on the sack such that the net force becomes (40-10) N downward (because downward force is more)
This net downward force is the resultant of earth graviational pull and the applied upward force.
So, this downward force acts on the machine which inturn applies an upaward force of same magnitude called Normal reaction.
This situation can be diagramatically represented by figure given below
Answer:
40N
Explanation:
trust
Two protons are a distance 3 10-9 m apart. What is the electric potential energy of the system consisting of the two protons
Answer:
The electric potential energy of the system is 7.87x10⁻²⁰ J.
Explanation:
The electric potential energy is given by:
[tex]E = \int{Fdr} = \frac{Kq_{1}q_{2}}{r}[/tex]
Where:
q₁ = q₂ is the charge of the protons = 1.62x10⁻¹⁹ C
r is the distance = 3x10⁻⁹ m
K: is the electrostatic constant = 9x10⁹ Nm²/C²
[tex] E = \frac{Kq_{1}q_{2}}{r} = \frac{9\cdot 10^{9} Nm^{2}/C^{2}*(1.62 \cdot 10^{-19} C)^{2}}{3\cdot 10^{-9} m} = 7.87 \cdot 10^{-20} J [/tex]
Therefore, the electric potential energy of the system is 7.87x10⁻²⁰ J.
I hope it helps you!
The electric potential energy of the system should be 7.87x10⁻²⁰ J.
Calculation of the electric potential energy:SInce We know that
fdr = kq1q2/r
Here
q₁ = q₂ i.e. is the charge of the protons = 1.62x10⁻¹⁹ C
r should be the distance = 3x10⁻⁹ m
K should be the electrostatic constant = 9x10⁹ Nm²/C²
Now electric potential energy should be
= (9x10⁹ Nm²/C² * 1.62x10⁻¹⁹ C) / 3x10⁻⁹ m
= 7.87x10⁻²⁰ J.
hence, The electric potential energy of the system should be 7.87x10⁻²⁰ J.
learn more about energy here: https://brainly.com/question/17384612
how are s waves and p waves simuliar?
A.they shake the ground
B.they travel through liquids
C. they arrive at the same time
D.they shake the ground from side to side
Answer:
A
Explanation:
hope this helps
Pressure and temperature ______ with depth below Earth’s surface.
Answer:
Pressure increases as you move deeper below earth's surface.
Tempurature increases as you move deeper below earth's surface.
Hope this helps!
Explanation:
On a hot day, you sit on the edge of a pool and dip your feet into the water, causing changes to occur that are related to the physical and thermal properties of your feet and of the water. Select the statements that accurately describe what is happening, in terms of the heat and temperature of the objects and substances. There may be more than one accurate statement.
The true statements are;
Heat from your feet raises the temperature of the water.
Your feet transfer heat into the surrounding water, reducing the temperature of your feet. B and C
What are thermal changes?The term thermal changes has t do with the changes in the heat properties of the substance. We know that when you put your leg in water there is a thermal exchange between the water and your leg.
Owing to the fact that heat is transferred from your leg to the water, your leg will feel cool while the temperature of the water will increase slightly.
Having said all these, the true statements are;
Heat from your feet raises the temperature of the water.
Your feet transfer heat into the surrounding water, reducing the temperature of your feet.
Learn more about thermal exchange:https://brainly.com/question/7230756
#SPJ1
Missing parts;
On a hot day, you sit on the edge of a pool and dip your feet into the water, causing changes to occur that are
related to the physical and thermal properties of your feet and of the water. Select the statements that
accurately describe what is happening, in terms of the heat and temperature of the objects and substances.
There may be more than one accurate statement.
A. Cold from the water reduces the temperature of your feet.
B. Heat from your feet raises the temperature of the water.
C. Your feet transfer heat into the surrounding water, reducing the temperature of your feet.
D. Cold from the water moves into your warm feet.
How do I proton and and electron compared
A person following a liberal ideology would likely approve of
a Venus fly trap is an......... plant.
Answer:
A Venus flytrap is a perennial carnivorous plant.
I hope it helps
plant that eats meat
Who ever answers first get Brainliest!
How is power passed down in a dynasty?
through a family bloodline
through a religious council
through an arranged marriage
through a military commander
Peter is running laps around a circular track with a diameter of 100 meters. If it takes Peter 12 minutes to run 4 laps, how quickly is he running (in meters per second)?
Answer:
v = 1.74 m/s
Explanation:
Given that,
Diameter of a circular track, d = 100 m
Distance covered for the 4 laps,
[tex]D=4\pi d\\\\D=4\pi \times 100\\\\D=1256.63\ m[/tex]
Time, t = 12 minutes = 720 s
We need to find the velocity of the peter. It can be calculated as follows :
[tex]v=\dfrac{D}{t}\\\\v=\dfrac{1256.63\ m}{720\ s}\\\\v=1.74\ m/s[/tex]
So, the speed is running with a velocity of 1.74 m/s.
Peter is running at 1.7453 m/sec.
Given to us,
Diameter of the circular track, D = 100 meters,
Number of laps Peter run, L = 4 laps,
Time taken by Peter, t = 12 minutes,
1 lap = circumference of the circle,
4 laps = 4 x circumference of the circle,
As we know, the circumference of a circle is given by πD.
So, 4 laps = 4 x circumference of the circle,
[tex]\begin{aligned}4 laps &= 4\times \pi \times D\\&= 4 \times \pi \times 100\\& = 1,256.6370\ meters\\\end{aligned}[/tex]
Also, we know that 1 minute has 60 sec.
so, 4 minutes = (4 x 60) seconds
Further, speed is given [tex]\bold{(\dfrac{Distance}{Time} )}[/tex]
Thus,
[tex]\begin{aligned}speed &= \dfrac{Distance\ coverd\ by\ Peter}{Time\ taken\ by\ Peter}\\&=\dfrac{1,256.6370}{12\times 60}\\&=1.7453\ m/sec \end{aligned}[/tex]
Hence, Peter is running at 1.7453 m/sec.
To know more visit:
https://brainly.com/question/7359669
A car starts from rest and accelerates for 7.2 s with an acceleration of 1.4 m/s2. How far does it travel? Answer in units of m.
Answer:
xn = 36.28 [m]
Explanation:
To solve this problem we must use the following equation of kinematics, which is ideal for a body that moves with constant acceleration.
[tex]x=x_{0}+(v_{o} *t)+(\frac{1}{2} )*a*t^{2}[/tex]
where:
x - xo = displacement of the car [m]
Vo = initial velocity = 0
t = time = 7.2 [s]
a = acceleration = 1.4 [m/s^2]
The initial velocity is zero, as the car begins its movement from rest.
xn = (x - xo), Now replacing
xn = (0*7.2) + 0.5*1.4*(7.2^2)
xn = 36.28 [m]
During which process of the water cycle does water change from a gas to liquad
A football team lost 3 yards on their first play. On the second play, 10 yards were gained. On the third play the quarterback got tackled behind the line of scrimmage and lost 6 yards. What was their net gain or loss after the three plays?
+1yd
Explanation:
Kfgjjh
Answer:
+1 YD
Explanation:
-3 + 10 - 6 = 1
A fountain shoots a jetof water straight up. The nozzle is 1 cm in diameter and the speed of the water exiting the nozzle is 30 m/s. What is the force exerted by the water jet
Answer:
Explanation:
mass of water coming out per second = A x v where A is area of cross section of the nozzle and v is velocity of water
A = 3.14 x .005²
= 785 x 10⁻⁷ m²
mass of water coming out per second = 785 x 10⁻⁷ x 30 = 23.55 x 10⁻⁴ kg
momentum of this mass = 23.55 x 10⁻⁴ x 30 = 706.5 x 10⁻⁴ kg m /s .
Rate of change of momentum = 706.5 x 10⁻⁴
Let force be F
F - mg = 706.5 x 10⁻⁴
F = mg + 706.5 x 10⁻⁴
F = 23.55 x 10⁻⁴ x 9.8 + 706.5 x 10⁻⁴
= 937.3 x 10⁻⁴ N .
(iii) Why do right angle mirrors produce three images of the object?
Explanation:
The two mirrors inclined to each other formed the first two images with are of the same size as the object while the third mirror is produced from the intersection of rays that emanated during the production of the first two images to produce a third image which is smaller than the object and there making the total number of images to be 3.
Hence this mirrors produces 3 images due to the third image formed from the intersection of the rays that produces the first two images.
The formula that relates the image produced by inclined mirror and the angle of inclination is expressed as:
number of images n = 360/θ - 1
θ is the angle of inclination of the two mirrors
n is the number of images
If the mirrors are inclined at right angles, then θ = 90°
Substitute into the formula;
n = 360/90 -1
n = 36/9 -1
n = 4-1
n = 3
Please provide explanation!!!
Thank you.
Answer:
(a) 102 cm/s
(b) 0.490 cm²
Explanation:
(a) Use Bernoulli equation.
P₁ + ½ ρ v₁² + ρgh₁ = P₂ + ½ ρ v₂² + ρgh₂
0 + ½ ρ v₁² + ρgh₁ = 0 + ½ ρ v₂² + 0
½ ρ v₁² + ρgh₁ = ½ ρ v₂²
½ v₁² + gh₁ = ½ v₂²
½ (25.0 cm/s)² + (980 cm/s²) (5.00 cm) = ½ v²
v = 102 cm/s
(b) The flow rate is constant.
v₁ A₁ = v₂ A₂
(25.0 cm/s) (2.00 cm²) = (102 cm/s) A
A = 0.490 cm²