The vector V is at a 72° angle and has a magnitude of 12.
Describe this vector using vector notation (Use the & and symbols.) (6 points)
Question 9
What is the angle of the vector described below? (3 points).
Please answer all questions will mark brainliest and give 5 stars
V=2x+3y
Answers
Answer:
Part 1
The vector can be expressed as follows;
r = 12, θ = 72°, ·v = (12, ∠72°), ·v ≈ 3.71·[tex]\mathbf{\hat i}[/tex] + 11.41·[tex]\mathbf{\hat j}[/tex] or
[tex]\mathbf{\cdot v}=\begin{bmatrix}3.71\\ 11.41\end{bmatrix} = \begin{pmatrix}3.71\\ 11.41 \end{pmatrix}[/tex]
Part 2
The angle of the vector is 56.31°
Explanation:
Part 1
The given parameters are;
The direction of the vector = 72°
The vector magnitude = 12
Therefore, the vector can be described in the following forms;
Polar form
1) Direct notation;
r = 12, θ = 72°
2) Ordered set
·v = (12, ∠72°)
Rectangular vector notation;
1) Unit vector notation
·v = vₓ[tex]\mathbf{\hat i}[/tex] + [tex]v_y[/tex][tex]\mathbf{\hat j}[/tex]
Where;
vₓ = 12 × cos(72) ≈ 3.71
[tex]v_y[/tex] = 12 × sin(72) ≈ 11.41
Therefore;
·v ≈ 3.71·[tex]\mathbf{\hat i}[/tex] + 11.41·[tex]\mathbf{\hat j}[/tex]
2) Matrix notation
[tex]\mathbf{\cdot v}=\begin{bmatrix}3.71\\ 11.41\end{bmatrix} = \begin{pmatrix}3.71\\ 11.41 \end{pmatrix}[/tex]
Part 2
The given vector is V = 2·x + 3·y
Therefore, the angle of the vector, θ = tan⁻¹(y/x) = tan⁻¹(3/2) ≈ 56.31°
The angle of the vector = 56.31°.
Related Questions
Embarking on a road trip, you hope to average a speed of 90.0 km/hr. Driving through bad weather, you finally reach the midpoint (half the distance) of your trip, but realize that you have only been averaging 5.0 X 10^1 km/hr. How fast would you have to drive the second half of the trip to keep your desired arrival time? *
Answers
Answer:
Explanation:
average speed = 90 km / hr
Let the total distance be 2 d .
time required to cover the time = 2 d / 90
time taken to cover distance d at 50 km /h = d / 50
time required to cover the nd half = 2 d / 90 - d / 50
.02222 d - .02 d = .002222 d
speed required = d/2 / .002222d
1 / 2 x .002222
= 225 km /h .
13. A baseball pitcher throws a fastball at a speed of 46m/s. The
acceleration occurs as the pitcher holds the ball in his hand and moves it
through an almost straight line distance of 3.5 m. Calculate the
acceleration, assume it is constant and uniform. (Answer in 3 sig figs and
do not include units) *
Answers
Answer: Approximately 302 m/s^2
================================================
Work Shown:
s = starting velocity = 0
f = final velocity = 46
d = distance = 3.5
a = acceleration = unknown (we're solving for this)
[tex]f^2 = s^2 + 2a*d \ \ \text{ ..... one of the kinematics equations}\\\\46^2 = 0^2 + 2a*3.5\\\\2116 = 7a\\\\7a = 2116\\\\a = \frac{2116}{7}\\\\a \approx 302.28571\\\\a \approx 302[/tex]
The acceleration to three sig figs is roughly 302 m/s^2
The acceleration is so large because the ball's final velocity is incredibly fast in such a short amount of time.
A student is given a 5.4 g mineral sample. She determines that the volume of her sample is 2 cm3. What is the density of her mineral
Answers
Answer:
6.7
Explanation:
Explain and reason why the the moon rotates around the earth every lunar cycle
Pls explain ASAP
Best answer will be marked as BRAINLIEST✨
Answers
otd-2)A softball is thrown straight up into the air at 25 m/s. if it returns to the thrower after 5.0 seconds, how high did it go?
Answers
One way:
The ball returned to the thrower's hand after 5 seconds. It spent 2.5 seconds going up, and 2.5 seconds coming back down.
Use the formula Distance = (1/2) (acceleration) (time squared)
Distance = (1/2) (gravity) (2.5 sec)
Distance = (1/2) (9.8 m/s ²) (6.25 sec² )
Distance = (4.9 m/s²) (6.25 sec²)
Distance = 30.63 meters
Another way:
The thrower threw the ball straight up at 25 m/s.
It sailed upward for 2.5 seconds.
At the top of its trip, before it started falling, its speed was zero.
Its average speed was (1/2) (25+0) = 12.5 m/s
At an average speed of 12.5 m/s for 2.5s, the ball rose (12.5x2.5) = 31.25m.
(Why are the two answers different ?
Because if the ball was thrown straight up at 25 m/s, it would actually return to the thrower in 5.1 seconds, not 5.0 seconds.
So if you use the acceleration of gravity to solve the problem, you get one answer, but if you use 5.0sec to solve it, you get a slightly different one.)
Which statement accurately describes a balanced force?
Answers
Answer:
a balanced force is when two forces equal each other out and therefor the object is not in motion.
Explanation:
Convert 6.6 meters to centimeters
Answers
Answer:
660 centimeters
Explanation:
There are 100 cm in 1 m. To convert from m to cm, multiply by 100.
[tex]6.6 \times 100 = 660[/tex]
There are 660 cm in 1 m.
hope this helps
If a bicyclist travels at 15 km/h, how long will it take her to travel 30 km?
Answers
At any given time in space, how much of
the moon is lit by the sun?
PLEASE ANSWER QUICKLY!!!
Answers
Answer: 50%
Explanation: The sun and the moon go around Earth and The sun is way bigger than the moon so 50% of the sun lights up the moon at night
Answer:
50%
Explanation:
MathPhys Pls PLS PLS PLS HELP ME!!!!
Which of these statements describes the relationship between mass and weight?
(1 Point)
Mass is always greater than weight.
Mass of an object changes based on location, weight stays constant.
Mass of an object is constant, weight changes based on location.
Mass and weight are the same measurement.
Answers
Answer:
Usually, the relationship between mass and weight on Earth is highly proportional; objects that are a hundred times more massive than a one-liter bottle of soda almost always weigh a hundred times more—approximately 1,000 newtons, which is the weight one would expect on Earth from an object with a mass slightly greater ...
Write a statement that explains the relationship among velocity, speed, and direction.
Answers
Answer:
velocity is the speed and direction of a moving object
Explanation:
that is basicaly the defention
If two cars are 5 m apart, and one car has a mass of 2,565 kg and the other
car has a mass of 4,264 kg, what is the gravitational force between the two
cars? Newton's law of gravitation is F gravity
Gm; m2 The gravitational
constant G is 6.67 x 10-11 Nm2/kg?.
A. 5.84 x 10-6N
B. 4.37 % 105 N.
C. 1.46 10-4N
D. 2.92 x 10-5 N
Answers
Gravitational force between two cars are 2.92 × 10 ⁻¹¹ Nm²/kg.
The universal force of attraction happened between two objects is called as gravitational force.
The mass of the two cars, m₁ = 2565 kg
m₂ = 4264 kg
r = 5m
G = 6.67 ₓ 10 ⁻11 Nm²/kg
How gravitational force can be calculated?
Definition of gravitational force: The force of attraction between any two bodies is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.
F ∝ m₁ m₂ ÷ r²
where the force exerted between the two masses m₁ and m₂,
F = G (m₁ m₂) ÷ r²
where as, F - Gravitational force between two bodies,
G - Gravitational constant,
m₁ - mass of the first body,
m₂ - mass of the second body,
r² - square of the distance between two bodies.
F= 6.67 × 10⁻¹¹ Nm²/kg ( 2565 kg × 4264 kg) ÷ ( 5²)
Hence,
F = 2.92 × 10⁻⁵ N
Option D is correct answer.
Learn more about Newton's law of Gravitation,
https://brainly.com/question/9373839
#SPJ5
A high school bus travels 240 km in 6.0 h. What is its average speed for the trip? (in km/h).
Answers
Answer:
40 km/h
Explanation:
First...
Look at the formula speed is equal to the distance over time or s = d/t.
Next...
Use the formula: 240/6.0
Finally...
Solve: 40
So the answer: 40 km/h
You use a knife to cut a piece of bread. What kind of simple machine are you
using?
A. Wedge
B. Inclined plane
C. Screw
O D. Lever
Answers
Answer:
the answer is A.) Wedge
A knife to cut a piece of bread is a A. Wedge
What is a simple machine?
A simple machine, any of several devices with few or no moving parts that are used to modify motion and the magnitude of a force in order to perform work.
since , a wedge is a simple machine with two inclined planes which when put together forms a sharped edge, which forms a triangular shaped tool which can be used to separate portion of two objects .
hence , a knife to cut a piece of bread is a A. Wedge
learn more about simple machine
https://brainly.com/question/10075890?referrer=searchResults
#SPJ2
Which energy source was developed through the invention of the atomic bomb?
Answers
Answer:
Nuclear energy
Explanation:
What force is needed to move a barrel 45-m if 3600 J of work are accomplished?
Answers
Answer:
The answer is 80 NExplanation:
The force acting on the object can be found by using the formula
[tex]f = \frac{w}{d} \\ [/tex]
where
d is the distance
w is the work done
We have
[tex]f = \frac{3600}{45} \\ [/tex]
We have the final answer as
80 NHope this helps you
The level of toluene (a flammable hydrocarbon) in a storage tank may fluctuate between 10 and 400 cm from the top of the tank. since it is impossible to see inside the tank, an open-end manometer with water or mercury as the manometer fluid is to be used to determine the toluene level. one leg of the manometer is attached to the tank 500 cm from the top. a nitrogen blanket at atmospheric pressure is maintained over the tank contents. felder, richard m.; rousseau, ronald w.; bullard, lisa g.. elementary principles of chemical processes, 4th edition (page 81). wiley. kindle edition.
Answers
Complete Question
The complete question is shown on the first and second uploaded image
Answer:
When water is used the reading is [tex] R = 2281.6 \ cm [/tex]
When mercury is used the reading is [tex] R = 23.83 \ cm [/tex]
The best fluid to use is mercury because for water a slight change in toluene level will cause a large change in height .
Explanation:
From the question we are told that
The length of the leg of the manometer to the top of the tank is d = 500cm
The toluene level where in the tank where the height of the manometer fluid level in the open arm is equal to the height where the manometer is connected to the tank is h =150 cm
The manometer reading is R
Generally at the point where the height of the open arm is equal to the height of the of the point connected to the tank ,
The pressure at the height of the both arms of the manometer corresponding to the base of the tank are equal
i.e [tex]P_1 = P_2[/tex]
Here [tex]P_1[/tex] is the pressure of the manometer at the point corresponding to the base of the tank and this is mathematically represented as
[tex] P_{atm} + P_1 = P_{atm} + P_t[/tex]
Here [tex]P_t[/tex] is the pressure due to the toluene level in the tank and in the arm of the manometer connected to the tank and this is mathematically represented as
[tex]P_t = \rho_t * g * h_i[/tex]
Here
[tex]\rho_t [/tex] is the density of toluene with value [tex]\rho_t = 867 kg/m^3 [/tex]
[tex]h_i[/tex] is the height of the connected arm above the point equivalent to the base of the tank , this mathematically represented as
[tex]h_i = d - h + R[/tex]
and [tex] P_2 [/tex] is the the pressure at the open arm of the manometer at the point equivalent to the base of the base of the tank and this is mathematically represented as
[tex] P_2 = \rho_f * g * h_f [/tex]
Here
[tex]\rho_f[/tex] is the density of the fluid in use , if it is water the density is
[tex]\rho_w = 1000 \ kg /m^3 [/tex]
and if it is mercury the density is
[tex]\rho_m = 13600 \ kg /m^3 [/tex]
[tex]h_f[/tex] is the height of the fluid in the open arm of the manometer from the point equivalent to the base of the tank which is equivalent the manometer reading R
So when the fluid is water we have
[tex] P_{atm} + \rho_t* g *(d - h + R) = P_{atm} + \rho_f * g * h_f[/tex]
=> [tex] \rho_t* (d - h + R) = \rho_w * h_f[/tex]
=> [tex] 867 (500 - 150 + R) = 1000 * R [/tex]
=> [tex] R = 2281.6 \ cm [/tex]
So when the fluid is mercury we have
[tex] \rho_t* (d - h + R) = \rho_m * h_f[/tex]
=> [tex] 867 (500 - 150 + R) = 13600 * R [/tex]
=> [tex] R = 23.83 \ cm [/tex]
The difference in the mercury reading for mercury due to the fact that they have different densities as we have seen in this calculation
So the best fluid to use is mercury because for water a slight change in toluene level will cause a large change in height .
What is better for measuring how hard you are actually working, Target Heart Rate or Rating of perceived exertion?
Answers
Answer:
Rating of percieved exertion
Muscles covert chemicals energy int
Answers
Answer:
Mechanical energy
Explanation:
Mechanical energy is needed for movement of objects. Muscles convert chemical energy provided by the rest of the body to allow movement.
The MSDS for chloroform indicates that it is a clear liquid that has a pleasant smell and substantial vapor pressure. People should avoid inhaling its vapors, and it is sensitive to light. Malik needs 10 mls of chloroform for an experiment.
According to this information, how should he safely pour the chloroform?
He should locate the chloroform stored in a transparent container in chemical storage and pour directly into his beaker from that location.
He should locate the chloroform stored in a transparent container in chemical storage and should take it to the fume hood to pour.
He should locate the chloroform stored in a dark container in chemical storage and should take it to the fume hood to pour.
He should locate the chloroform stored in a dark container in chemical storage and pour directly into his beaker from that location.
Answers
Answer:
The correct option is the third option
Explanation:
Firstly, it must be noted that chemicals/reagents that are sensitive to sunlight are stored in dark/amber container in the laboratory. Hence, the chloroform can only be found in an amber/dark bottle.
Also, reagents/chemicals that release poisonous/offensive gases are handled in the fume cupboard in the laboratory. Thus, If Malik is going to pour the chloroform, he should pour it in a fume cupboard to avoid inhaling it because of the toxicity of it's vapor.
From the above explanation, it can be deduced that Malik should locate the chloroform stored in a dark container in chemical storage and should take it to the fume hood to pour.
Answer:
He should locate the chloroform stored in a dark container in chemical storage and should take it to the fume hood to pour.
Explanation:
1. If a ball is rolling horizontally on the floor with a velocity of 2.5 m/s, what are the x and y
components of the velocity?
Vx =
Vy =
Answers
Answer: Vx = 2.5m/s and Vy = 0m/s
Explanation: The ball is rolling horizontally on the floor, meaning there isn't a change in the vertical position, only horizontal. The ball is rolling with pure horizontal motion and isn't moving in the vertical direction.
Is a cookie crumbling or in other words breaking a cookie a physical change?
Answers
Answer:
Yes it is a physical change
Explanation:
The cookie is still a cookie even when it has been broken apart, so it cannot be a chemical change. The cookie only changed physically.
Describe effect of artificial selection on the process of evolution
Answers
Answer: The process is called artificial selection because people (instead of nature) select which organisms get to reproduce.
Explanation: This is evolution through artificial selection and the characteristics to reproduce, causing the evolution of farm stock.
How long will it take a car to go from a complete stop to 44 km/hr if they are accelerating at 5 km/hr^2
Answers
Answer:
8.8 hours
Explanation:
plz give me a Brainliest
Which of the three objects is the largest? Explain your answer.
Answers
Answer:
isn't it the first one
Answer:
The object in figure C is a planet, so it is the largest object. Planets are larger than comets and asteroids.
Explanation:
what is the role of energy in the conversation about climate change?
Answers
Answer:
Energy plays an important role in many aspects of our lives. For example, we use electricity for lighting and cooling.
Explanation:
Answer:
engery
Explanation:
A ball is thrown horizontally from the top of
a building 51 m high. The ball strikes the
ground at a point 120 m from the base of the
building.
The acceleration of gravity is 9.8 m/s
2
.
Find the time the ball is in motion.
Answer in units of s.
If the time the ball is in motion is 3.22617 s
Find the initial velocity of the ball.
Answer in units of m/s.
Answers
Answer:
whattt
Explanation:
sorry dear I did not understandWhen a light ray enters water, its velocity is _________.
Answers
Answer:
UR ANSWER IS WAVELENGTH
A runner is jogging in a straight line at a steady vr= 7.3 km/hr. When the runner is L= 2.1 km from the finish line, a bird begins flying straight from the runner to the finish line at vb= 29.2 km/hr (4 times as fast as the runner). When the bird reaches the finish line, it turns around and flies directly back to the runner After this first encounter, the bird then turns around and flies from the runner back to the finish line, turns around again and flies back to the runner. The bird repeats the back and forth trips until the runner reaches the finish line. How far does the bird travel from the beginning (including the distance traveled to the first encounter
Answers
Answer:
Explanation:
Time taken by jogger to travel the distance to finishing line = 2.1 / 7.3
= .28767 hr
Bird will keep flying for this time period
distance covered by bird = speed x time
= 29.2 x .28767 km
= 8.4 km .
How much time will it take a truck to go from 10 m/s to 35 m/s if the truck accelerates at a constant rate of 1.7 m/s2 ?
Answers
Answer:
thank u for the happiest year of my life