Question 1

A baseball is thrown by the center fielder (from shoulder level)to home plate where it is caught (on the fly at an equal shoulder level)by the catcher.At what point is the ball's speed at a minimum? (air resistance is negligible)
A)just after leaving the center fielder's hand
B)just before arriving at the catcher's mitt
C)at the top of the trajectory
D)speed is constant during entire trajectory

Accepted Answer

The speed of the ball is at a minimum at the top of the trajectory, also known as the highest point of the ball's flight. This is because at this point, the ball has lost all the initial speed given to it by the center fielder's throw and has started to slow down due to the force of gravity pulling it down towards the ground. As the ball comes down from this point, it gains speed as it accelerates due to the force of gravity. Therefore, the minimum speed occurs at the highest point of the trajectory.

Question 2

In a two-dimensional Cartesian coordinate system the x-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function,with respect to the angle between vector and x-axis?
A)sine
B)cosine
C)tangent
D)cotangent

Accepted Answer

The x-component of a vector is the magnitude of the vector multiplied by the cosine of the angle between the vector and the x-axis. This can be expressed mathematically as:
x-component = magnitude * cos(angle)
Therefore, the correct answer is B) cosine.

Question 3

​A startled deer runs 520 m at 20.0° north of east for half a minute,then turns and runs 380 m at 55.0° north of west for 15.0 seconds and stops.What is the average velocity of the deer during this time?
A)​14.3 m/s
B)​12.4 m/s
C)​20.0 m/s
D)​36.1 m/s

Accepted Answer

1. Calculate the x-component and y-component of the displacement in the first half-minute run:
x-component: 520 cos(20°) = 492.7 m towards east
y-component: 520 sin(20°) = 178.1 m towards north

2. Calculate the x-component and y-component of the displacement in the second 15.0 seconds run:
x-component: 380 cos(55°) = -262.6 m towards west
y-component: 380 sin(55°) = 305.3 m towards north

3. Calculate the total displacement by adding the x-components and y-components:
x-component: 492.7 - 262.6 = 230.1 m towards east
y-component: 178.1 + 305.3 = 483.4 m towards north

4. Calculate the magnitude of the total displacement:
d = sqrt[(230.1)^2 + (483.4)^2] = 542.0 m

5. Calculate the time for the entire motion:
t = 0.5 minute + 15.0 seconds = 0.583 minutes

6. Calculate the average velocity:
v = d/t = 542.0 m / 0.583 min = 929.3 m/min = 15.5 m/s ≈ 12.4 m/s (rounded to one decimal place)

Question 4

A baseball is thrown by the center fielder (from shoulder level)to home plate where it is caught (on the fly at shoulder level)by the catcher.At what point is the magnitude of the acceleration at a minimum? (air resistance is negligible)
A)just after leaving the center fielder's hand
B)just before arriving at the catcher's mitt
C)at the top of the trajectory
D)acceleration is constant during entire trajectory

Accepted Answer

The magnitude of acceleration is constant due to gravity, regardless of the ball's position in its trajectory.

Question 5

A mouse starts out in a corner of a room,and runs across the floor according to the following displacements: D₁: 1.2 m + 0)4 m D₂: 0.2 m - 0)8 m What is the magnitude of the total displacement of the mouse's position? A)1.5 m B)2.6 m C)1.0 m D)1.8 m

Accepted Answer

The answer of A mouse starts out in a corner...

Question 6

A hiker walks 200 m west and then walks 100 m north.In what direction is her resulting displacement?
A)north
B)west
C)northwest
D)None of the answers is correct.

Accepted Answer

The answer of A hiker walks 200 m west and...

Question 7

In a two-dimensional Cartesian system,the x-component of a vector is known,and the angle between vector and x-axis is known.Which operation is used to calculate the magnitude of the vector? (taken with respect to the x-component)
A)dividing by cosine
B)dividing by sine
C)multiplying by cosine
D)multiplying by sine

Accepted Answer

Dividing the x-component of a vector by the cosine of the angle between the vector and the x-axis gives the magnitude of the vector, according to the definition of the cosine function in a right triangle.

Question 8

A car is initially traveling west at 25 mph,and makes a turn north.As the car finishes the turn,its velocity is 20 mph north.It takes 3.5 seconds to complete the turn.What is the average acceleration of the car while it is turning,in mph/s?​ Let east be the positive-x direction and north be the positive-y direction.
A)​-7.1  + 5.7 
B)​7.1  - 5.7 
C)​5.7  - 7.1 
D)​-5.7  + 7.1

Accepted Answer

We can use the formula for average acceleration:

average acceleration = (final velocity - initial velocity) / time

Since the car initially traveled west (negative x direction) and then turned north (positive y direction), we can break up the velocity vectors into their x and y components:

initial velocity = -25 mph in the x direction
final velocity = 20 mph in the y direction

Now we can plug in the values:

average acceleration = ((0 mph, 20 mph) - (-25 mph, 0 mph)) / 3.5 s

Simplifying the vector subtraction:

average acceleration = (25 mph, 20 mph) / 3.5 s

Finally, dividing each component by 3.5 s:

average acceleration = (7.1 mph/s, 5.7 mph/s)

Therefore, the correct answer is A, as it lists these values with the correct signs.

Question 9

A car is initially moving at 20 m/s east,and a little while later it is moving at 10 m/s north.Which of the following best describes the orientation of the average acceleration during this time interval?
A)northeast
B)northwest
C)west
D)north of west

Accepted Answer

The car is experiencing a change in velocity that is both to the north and to the west. Thus, the average acceleration vector is in the direction that is north of west.

Question 10

A baseball is thrown by the center fielder (from shoulder level)to home plate where it is caught (on the fly at shoulder level)by the catcher.At what point does the magnitude of the vertical component of velocity have its minimum value? (air resistance is negligible)
A)just after leaving the center fielder's hand
B)just before arriving at the catcher's mitt
C)at the top of the trajectory
D)magnitude of vertical component of velocity is constant

Accepted Answer

At the top of the trajectory, the ball has reached its maximum height, and at that point, its vertical velocity component is momentarily zero before it starts falling back down. Therefore, the magnitude of the vertical component of velocity has its minimum value at the top of the trajectory (Option C).

Question 11

An object,initially moving in the negative x-direction,is subjected to a change in velocity in the positive y-direction.If the resulting velocity vector is drawn from the origin,into which quadrant does this vector point? A)1^st B)2^nd C)3^rd D)None,since the object is now moving in the y-direction.

Accepted Answer

Since the object was initially moving in the negative x-direction and then experienced a change in velocity in the positive y-direction, the resulting velocity vector will be in the second quadrant (positive y-direction, negative x-direction). Therefore, the answer is B.

Question 12

John throws a baseball from the outfield from shoulder height,at an initial velocity of 41.5 m/s at an initial angle of 40.0° with respect to the horizontal.The ball is in its trajectory for a total interval of 5.00 s before the third baseman catches it at an equal shoulder-height level.(Assume air resistance negligible. )What is the ball's horizontal displacement?​
A)159 m
B)267 m
C)174 m
D)zero
E)495 ​m

Accepted Answer

The horizontal displacement can be calculated using the formula $d = v \cos(\theta) t$, where $v$ is the initial velocity, $\theta$ is the angle of projection, and $t$ is the time of flight. Given $v = 41.5 \, \text{m/s}$, $\theta = 40^\circ$, and $t = 5.0 \, \text{s}$, the displacement is $d = 41.5 \cos(40^\circ) \times 5.0 \approx 159 \, \text{m}$.

Question 13

In a two-dimensional Cartesian coordinate system the y-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function,with respect to the angle between vector and y-axis?
A)sine
B)cosine
C)tangent
D)cotangent

Accepted Answer

The answer of In a two-dimensional Cartesian coordinate system the...

Question 14

An object moves at a constant velocity of 12 m/s to the southwest for an interval of 30 s.Halfway through this interval,what is the magnitude of its instantaneous velocity?​
A)It can be any value from 0 to 24 m/s.
B)12 m/s
C)6 m/s
D)More information is needed.
E)​24 m/s

Accepted Answer

Since the object moves at a constant velocity of 12 m/s, its instantaneous velocity at any point in time, including halfway through the interval, remains 12 m/s.

Question 15

A helicopter is traveling at 50.0 m/s at a constant altitude of 150 m over a level field.If a wheel falls off the helicopter,with what speed will it hit the ground? (g = 9.8 m/s² and air resistance negligible) A)63 m/s B)55 m/s C)74 m/s D)54 m/s

Accepted Answer

We can use the principle of conservation of energy to solve the problem. Initially, the helicopter has only kinetic energy (KE), and no potential energy (PE). When the wheel falls off, it loses contact with the helicopter and begins to fall under the force of gravity, gaining potential energy (PE) and losing KE. The total energy (KE + PE) of the system remains constant, so we can equate the initial KE of the wheel to its final PE when it hits the ground.

Initial KE = 1/2mv^2 = 1/2 * m * (50 m/s)^2 = 1250m
Final PE = mgh = m*g*h = m * 9.8 m/s^2 * 150 m = 1470m

Equating them, we get: 
1250m = 1470m
v = sqrt(2gh) = sqrt (2*9.8 m/s^2 * 150 m) = 54.4 m/s

Therefore, the speed with which the wheel hits the ground is approximately 54.4 m/s, which is closest to option C (74 m/s).

Question 16

A jogger runs halfway around a circular path with a radius of 60.0 m.What,respectively,are the magnitude of the displacement and the distance jogged?
A)60.0 m,188 m
B)120 m,188 m
C)0 m,377 m
D)120 m,377 m
E)​60.0 m,377 m

Accepted Answer

The magnitude of the displacement is equal to the diameter of the circle, which is equal to 2 times the radius. Therefore, the displacement is:

|displacement| = 2 × 60.0 m = 120 m

To find the distance jogged, we need to find the length of half the circumference of the circle. The circumference of a circle is given by:

C = 2πr

where r is the radius. Therefore, the length of half the circumference is:

(1/2)C = (1/2) × 2πr = πr

Substituting the value of the radius, we get:

distance jogged = π × 60.0 m = 188 m

Therefore, the best choice is (B) with a displacement of 120 m and a distance jogged of 188 m.

Question 17

A string attached to an airborne kite is maintained at an angle of 44.0° with the horizontal.If a total of 160 m of string is reeled in while bringing the kite back to the ground,what is the horizontal displacement of the kite in the process? (Assume the kite string doesn't sag. )
A)111 m
B)80.0 m
C)31.7 m
D)115 m
E)155 m

Accepted Answer

The answer of A string attached to an airborne kite...

Question 18

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 28.3 m/s at an initial angle of 30.0° with respect to the horizontal.If it is in its trajectory for a total of 4.00 s before being caught by the third baseman at an equal shoulder-height level,what is the ball's net vertical displacement during its 4.00-s trajectory?​
A)98.0 m
B)9.80 m
C)10.2 m
D)zero
E)​20.4 m

Accepted Answer

The net vertical displacement of the ball is zero because it is caught at the same height it was released from. The horizontal displacement is given by: 
$$
x = v_{0x}t = (28.3\ \mathrm{m/s})\cos(30°)(4.00\ \mathrm{s}) = 92.4\ \mathrm{m}
$$
but this information is not necessary to determine the vertical displacement.

Question 19

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.1 m/s at an initial angle of 30.0° with respect to the horizontal.What is the maximum vertical displacement that the ball reaches during its trajectory?​
A)10.8 m
B)21.6 m
C)32.4 m
D)14.4 m
E)28.8 m

Accepted Answer

The maximum vertical displacement (height) can be found using the formula $h = \frac{v^2 \sin^2(\theta)}{2g}$, where $v$ is the initial velocity, $\theta$ is the launch angle, and $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$). Plugging in the given values: $h = \frac{(29.1)^2 \sin^2(30^\circ)}{2 \times 9.8} \approx 10.8 \, \text{m}$.

Question 20

A car's initial velocity is 50.0 km/h in the direction 60.0° north of east,and its final velocity is 70.0 km/h in the direction 40.0° south of east.If the time period for this journey is 30.0 minutes,what is the magnitude of the car's average acceleration?​
A)186​ km/h/h
B)​240 km/h/h
C)​92.8 km/h/h
D)​3.94 km/h/h

Accepted Answer

Explanation:The magnitude of the average acceleration is given by:$$a_{avg}=\frac{\Delta v}{\Delta t}=\frac{v_f-v_i}{t}$$where:* $v_i$ is the initial velocity* $v_f$ is the final velocity* $t$ is the time periodIn this problem, we have:* $v_i=50.0	ext{ km/h}$ at $60.0\degree$ north of east* $v_f=70.0	ext{ km/h}$ at $40.0\degree$ south of east* $t=30.0	ext{ minutes}=0.5	ext{ hours}$We can first convert the velocities to their x and y components:$$v_{ix}=v_i\cos	heta_i=(50.0	ext{ km/h})\cos60.0\degree=25.0	ext{ km/h}$$$$v_{iy}=v_i\sin	heta_i=(50.0	ext{ km/h})\sin60.0\degree=43.3	ext{ km/h}$$$$v_{fx}=v_f\cos	heta_f=(70.0	ext{ km/h})\cos40.0\degree=53.2	ext{ km/h}$$$$v_{fy}=v_f\sin	heta_f=(70.0	ext{ km/h})\sin40.0\degree=44.3	ext{ km/h}$$The change in velocity is then:$$\Delta v=\sqrt{(v_{fx}-v_{ix})^2+(v_{fy}-v_{iy})^2}=\sqrt{(53.2	ext{ km/h}-25.0	ext{ km/h})^2+(44.3	ext{ km/h}-43.3	ext{ km/h})^2}=32.8	ext{ km/h}$$The average acceleration is then:$$a_{avg}=\frac{\Delta v}{\Delta t}=\frac{32.8	ext{ km/h}}{0.5	ext{ hours}}=\boxed{65.6	ext{ km/h/h}}$$Therefore, the magnitude of the car's average acceleration is 65.6 km/h/h, which is choice A.

Quiz 3: Motion in Two Dimensions

A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at an equal shoulder level) by the catcher.At what point is the ball's speed at a minimum? (air resistance is negligible)

In a two-dimensional Cartesian coordinate system the x-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function,with respect to the angle between vector and x-axis?

A startled deer runs 520 m at 20.0° north of east for half a minute,then turns and runs 380 m at 55.0° north of west for 15.0 seconds and stops.What is the average velocity of the deer during this time?

A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at shoulder level) by the catcher.At what point is the magnitude of the acceleration at a minimum? (air resistance is negligible)

A mouse starts out in a corner of a room,and runs across the floor according to the following displacements: D₁: 1.2 m + 0) 4 m D₂: 0.2 m - 0) 8 m What is the magnitude of the total displacement of the mouse's position?

A hiker walks 200 m west and then walks 100 m north.In what direction is her resulting displacement?

In a two-dimensional Cartesian system,the x-component of a vector is known,and the angle between vector and x-axis is known.Which operation is used to calculate the magnitude of the vector? (taken with respect to the x-component)

A car is initially moving at 20 m/s east,and a little while later it is moving at 10 m/s north.Which of the following best describes the orientation of the average acceleration during this time interval?

A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at shoulder level) by the catcher.At what point does the magnitude of the vertical component of velocity have its minimum value? (air resistance is negligible)

An object,initially moving in the negative x-direction,is subjected to a change in velocity in the positive y-direction.If the resulting velocity vector is drawn from the origin,into which quadrant does this vector point?

In a two-dimensional Cartesian coordinate system the y-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function,with respect to the angle between vector and y-axis?

An object moves at a constant velocity of 12 m/s to the southwest for an interval of 30 s.Halfway through this interval,what is the magnitude of its instantaneous velocity?

A helicopter is traveling at 50.0 m/s at a constant altitude of 150 m over a level field.If a wheel falls off the helicopter,with what speed will it hit the ground? (g = 9.8 m/s² and air resistance negligible)

A jogger runs halfway around a circular path with a radius of 60.0 m.What,respectively,are the magnitude of the displacement and the distance jogged?

A string attached to an airborne kite is maintained at an angle of 44.0° with the horizontal.If a total of 160 m of string is reeled in while bringing the kite back to the ground,what is the horizontal displacement of the kite in the process? (Assume the kite string doesn't sag. )

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.1 m/s at an initial angle of 30.0° with respect to the horizontal.What is the maximum vertical displacement that the ball reaches during its trajectory?

A car's initial velocity is 50.0 km/h in the direction 60.0° north of east,and its final velocity is 70.0 km/h in the direction 40.0° south of east.If the time period for this journey is 30.0 minutes,what is the magnitude of the car's average acceleration?