Question 1

A package is dropped from a helicopter that is moving upward at $15 \mathrm {~m} / \mathrm { s }$ If it takes $8.0 \mathrm {~s}$ before the package strikes the ground, how high above the ground was the package when it was released? Neglect air resistance.

Accepted Answer

The answer of A package is dropped from a helicopter...

Question 2

A ball is thrown straight up with a speed of 30 m/s, and air resistance is negligible.
(a) How long does it take the ball to reach the maximum height?
(b) What is the maximum height reached by the ball?
(c) What is its speed after 4.2 s?

Accepted Answer

The answer of A ball is thrown straight up with...

Question 3

A foul ball is hit straight up into the air with a speed of 30 m/s, and air resistance is negligible.
(a) Calculate the time required for the ball to rise to its maximum height.
(b) Calculate the maximum height reached by the ball above the point where it hit the bat.
(c) Determine the times at which the ball passes a point 25 m above the point where it was hit by the bat.
(d) Explain why there are two answers to part (c).

Accepted Answer

The answer of A foul ball is hit straight up...

Question 4

A ball is thrown upward at a velocity of 19.6 m/s. What is its velocity after 3.0 s, assuming negligible air resistance?

Accepted Answer

The velocity of the ball after 3.0 s can be calculated using the equation $v = u + at$, where $v$ is the final velocity, $u$ is the initial velocity (19.6 m/s upward), $a$ is the acceleration due to gravity (-9.8 m/s$^2$ downward), and $t$ is the time (3.0 s). Plugging in the values, we get $v = 19.6 m/s - (9.8 m/s^2 \times 3.0 s) = 19.6 m/s - 29.4 m/s = -9.8 m/s$, indicating a velocity of 9.8 m/s downward.

Question 5

A rock is projected upward from the surface of the Moon, at time t = 0 s, with an upward velocity of 30.0 m/s. The acceleration due to gravity at the surface of the Moon is 1.62 m/s², and the Moon has no atmosphere. The height of the rock when it is descending with a speed of 20.0 m/s is closest to

Accepted Answer

We can use the kinematic equation:

v_f^2 = v_i^2 + 2ad

where v_f is the final velocity (20.0 m/s), v_i is the initial velocity (30.0 m/s), a is the acceleration due to gravity on the Moon (-1.62 m/s^2), and d is the distance traveled.

Solving for d, we get:

d = (v_f^2 - v_i^2)/(2a)
  = (20.0^2 - 30.0^2)/(2*(-1.62))
  = 154.32 m

Therefore, the height of the rock when it is descending with a speed of 20.0 m/s is closest to 154 m. The best choice is E.

Question 6

A bullet shot straight up returns to its starting point in 10 s. What is the initial speed of the bullet, assuming negligible air resistance?

Accepted Answer

Using the kinematic equation s = ut + 1/2 at^2, we can find the displacement of the bullet during the first half of its trajectory (from release to maximum height) and use this to determine the initial velocity. 
For the first half of the motion, the displacement is given by: 
s = 1/2 gt^2 (where g is the acceleration due to gravity) 
Since the total flight time is 10 seconds, the time to reach maximum height is 5 seconds. Thus, the displacement during this time is: 
s = 1/2 (9.8 m/s^2)(5 s)^2
s = 122.5 m

Since the bullet returns to its starting point, the displacement for the entire motion is zero. Therefore, the displacement during the second half of the motion (from maximum height to release) is also 122.5 m. Using the same kinematic equation, we have:

-122.5 m = (u)(-5 s) + 1/2 (-9.8 m/s^2)(-5 s)^2

Simplifying, we get:

u = 49 m/s

Therefore, the initial speed of the bullet is 49 m/s, which is answer choice C.

Question 7

At the same moment, one rock is dropped and one is thrown downward with an initial velocity of $29 \mathrm {~m} / \mathrm { s }$ from the top of a building that is $300 \mathrm {~m}$ tall. How much earlier does the thrown rock strike the ground? Neglect air resistance.

Accepted Answer

The answer of At the same moment, one rock is...

Question 8

Human reaction time is usually greater than 0.10 s. If your friend holds a ruler between your fingers and releases it without warning, how far can you expect the ruler to fall before you catch it, assuming negligible air resistance?

Accepted Answer

Assuming negligible air resistance, the ruler will fall freely with an acceleration of g = 9.8 m/s². During the time it takes for a person to react and catch the ruler, the ruler will have fallen the distance d given by:
d = 1/2 * g * t²
Where t is the reaction time. Given that human reaction time is usually greater than 0.10 s, we have:
t = 0.10 s
So, d = 1/2 * 9.8 m/s² * (0.10 s)² = 0.049 m = 4.9 cm. Therefore, the answer is B.

Question 9

A toy rocket is launched vertically from ground level at time t = 0.00 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 81 m and acquired an upward velocity of $ 40 \mathrm{~m} / \mathrm{s} $ The rocket continues to rise with insignificant air resistance in unpowered flight, reaches maximum height, and falls back to the ground. The upward acceleration of the rocket during the burn phase is closest to

Accepted Answer

Using the kinematic equation $ v^2 = u^2 + 2as $, where $ v = 40 \, \mathrm{m/s} $, $ u = 0 \, \mathrm{m/s} $, and $ s = 81 \, \mathrm{m} $, we solve for $ a $: $ 40^2 = 0 + 2a \times 81 $. Solving gives $ a \approx 9.9 \, \mathrm{m/s}^2 $.

Question 10

A hammer is thrown upward with a speed of 14 m/s on the surface of planet X where the acceleration due to gravity is 3.5 m/s² and there is no atmosphere. What is the speed of the hammer after 8.0 s?

Accepted Answer

The answer of A hammer is thrown upward with a...

Question 11

A ball is thrown straight up with a speed of 36 m/s. How long does it take to return to its starting point, assuming negligible air resistance?

Accepted Answer

When a ball is thrown straight up, its initial velocity is positive and its final velocity is negative (when it returns to its starting point). Using the kinematic equation:

final velocity = initial velocity - acceleration x time

We can solve for time:

time = (final velocity - initial velocity) / acceleration

Since the acceleration due to gravity is constant (9.8 m/s^2) and the final velocity is equal in magnitude and opposite in direction to the initial velocity (36 m/s), we can simplify the equation:

time = (36 m/s - (-36 m/s)) / 9.8 m/s^2 = 7.3 s

Therefore, the answer is B.

Question 12

A ball is projected upward at time t = 0 s, from a point on a flat roof 10 m above the ground. The ball rises and then falls with insignificant air resistance, missing the roof, and strikes the ground. The initial velocity of the ball is $ 58.5 \mathrm{~m} / \mathrm{s} . $ Consider all quantities as positive in the upward direction. At time $ t=5.97 \mathrm{~s} $, the vertical velocity of the ball is closest to

Accepted Answer

The ball is at the highest point of its trajectory at time $ t=5.97 \mathrm{~s} $, so its vertical velocity is 0 m/s.

Question 13

A ball is thrown downward from the top of a building with an initial speed of 25 m/s. It strikes the ground after 2.0 s. How high is the building, assuming negligible air resistance?

Accepted Answer

Using kinematic equations, we can find the height of the building. Let's consider down as positive direction.
Initial velocity, u = 25 m/s (negative sign indicates it is moving downward)
Time taken, t = 2.0 s
Acceleration due to gravity, a = 9.81 m/s^2 (constant value)
Using the kinematic equation, s = ut + 0.5 at^2, we get
s = -25×2 + 0.5×9.81×2^2
s = -50 + 19.62
s = -30.38 m (negative sign indicates it is below the starting point)
Therefore, the height of the building is 30.38 m. 
But the question asks for "how high" and not "how deep" it is. Therefore, we take the absolute value of this result, which is 30.38 m. Thus, the best choice is D.

Question 14

A toy rocket is launched vertically from ground level at time t = 0.00 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 64 m and acquired an upward velocity of $ 60 \mathrm{~m} / \mathrm{s} $ The rocket continues to rise with insignificant air resistance in unpowered flight, reaches maximum height, and falls back to the ground. The time interval during which the rocket engine provided the upward acceleration, is closest to

Accepted Answer

The correct answer is A.The rocket's initial velocity is 0 m/s, and its final velocity at burnout is 60 m/s. The acceleration during the burn phase is:$$a = \frac{v_f - v_i}{t} = \frac{60 \mathrm{~m} / \mathrm{s} - 0 \mathrm{~m} / \mathrm{s}}{t}$$The rocket rises to a height of 64 m during the burn phase, so:$$d = v_i t + \frac{1}{2} a t^2 = 0 \mathrm{~m} + \frac{1}{2} a t^2$$Solving for t, we get:$$t = \sqrt{\frac{2d}{a}} = \sqrt{\frac{2(64 \mathrm{~m})}{a}}$$Substituting the expression for a, we get:$$t = \sqrt{\frac{2(64 \mathrm{~m})}{\frac{60 \mathrm{~m} / \mathrm{s} - 0 \mathrm{~m} / \mathrm{s}}{t}}}$$Solving for t, we get:$$t = 2.1 \mathrm{~s}$$

Question 15

A rock is thrown directly upward from the edge of a flat roof of a building that is 56.3 meters tall. The rock misses the building on its way down, and is observed to strike the ground 4.00 seconds after being thrown. Take the acceleration due to gravity to have magnitude $9.80 \mathrm {~m} / \mathrm { s } ^ { 2 }$ and neglect any effects of air resistance. With what speed was the rock thrown?

Accepted Answer

The answer of A rock is thrown directly upward from...

Question 16

A toy rocket is launched vertically from ground level at time t = 0 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 49.0 m and acquired an upward velocity of $60.0 \mathrm {~m} / \mathrm { s }$ The rocket continues to rise with insignificant air resistance in unpowered flight, reaches maximum height, and falls back to the ground. The maximum height reached by the rocket is closest to

Accepted Answer

The correct answer is A because the maximum height reached by the rocket is 233 m.

Question 17

An instrument is thrown upward with a speed of 15 m/s on the surface of planet X where the acceleration due to gravity is 2.5 m/s² and there is no atmosphere. How long does it take for the instrument to return to where it was thrown?

Accepted Answer

The answer of An instrument is thrown upward with a...

Question 18

A ball is thrown straight upward from ground level with a speed of $18 \mathrm {~m} / \mathrm { s }$ How much time passes before the ball strikes the ground if we disregard air resistance?

Accepted Answer

The time to reach the maximum height is $ t = \frac{v}{g} = \frac{18 \, \text{m/s}}{9.8 \, \text{m/s}^2} \approx 1.84 \, \text{s} $. The total time for the round trip is twice this, approximately $ 3.7 \, \text{s} $.

Question 19

A ball is projected upward at time t = 0 s, from a point on a flat roof 90 m above the ground. The ball rises and then falls with insignificant air resistance, missing the roof, and strikes the ground. The initial velocity of the ball is $ 80.5 \mathrm{~m} / \mathrm{s} $ Consider all quantities as positive in the upward direction. The vertical velocity of the ball when it is $ 89 \mathrm{~m} $ above the ground is closest to

Accepted Answer

The correct answer is A because the ball is moving upward with a velocity of 80.5 m/s when it is 90 m above the ground. As it rises, its velocity decreases due to gravity. When it is 89 m above the ground, its velocity is slightly less than 80.5 m/s, but still positive. As it continues to rise, its velocity will continue to decrease until it reaches a maximum height, at which point its velocity will be zero. Then, it will begin to fall, and its velocity will increase in the downward direction. When it is 89 m above the ground on the way down, its velocity will be approximately -81 m/s.

Question 20

A test rocket at ground level is fired straight up from rest with a net upward acceleration of 20 m/s². After 4.0 s, the motor turns off but the rocket continues to coast upward with insignificant air resistance. What maximum elevation does the rocket reach?

Accepted Answer

Using kinematic equations, we can find the maximum elevation of the rocket. 
First, we can find the velocity of the rocket after 4 seconds:
v = u + at
v = 0 + 20(4)
v = 80 m/s
Next, we can find the distance traveled by the rocket during those 4 seconds:
s = ut + 1/2at^2
s = 0(4) + 1/2(20)(4)^2
s = 160 m
Now, we can use the fact that the rocket is coasting upward with no acceleration to find the maximum elevation:
s = ut + 1/2at^2
0 = 80t + 1/2(-9.8)t^2    (since acceleration is now -g)
0 = 80t - 4.9t^2
0 = t(80 - 4.9t)
t = 16.33 s (using the quadratic formula)
Now we can find the maximum elevation:
s = ut + 1/2at^2
s = 80(16.33) + 1/2(-9.8)(16.33)^2
s = 490 m
Therefore, the answer is E, 490 m.

Quiz 2: Motion in One Dimension

A package is dropped from a helicopter that is moving upward at 15 m/s15 \mathrm {~m} / \mathrm { s }15 m/s If it takes 8.0 s8.0 \mathrm {~s}8.0 s before the package strikes the ground, how high above the ground was the package when it was released? Neglect air resistance.

A ball is thrown straight up with a speed of 30 m/s, and air resistance is negligible. (a) How long does it take the ball to reach the maximum height? (b) What is the maximum height reached by the ball? (c) What is its speed after 4.2 s?

A ball is thrown upward at a velocity of 19.6 m/s. What is its velocity after 3.0 s, assuming negligible air resistance?

A rock is projected upward from the surface of the Moon, at time t = 0 s, with an upward velocity of 30.0 m/s. The acceleration due to gravity at the surface of the Moon is 1.62 m/s2, and the Moon has no atmosphere. The height of the rock when it is descending with a speed of 20.0 m/s is closest to

A bullet shot straight up returns to its starting point in 10 s. What is the initial speed of the bullet, assuming negligible air resistance?

At the same moment, one rock is dropped and one is thrown downward with an initial velocity of 29 m/s29 \mathrm {~m} / \mathrm { s }29 m/s from the top of a building that is 300 m300 \mathrm {~m}300 m tall. How much earlier does the thrown rock strike the ground? Neglect air resistance.

Human reaction time is usually greater than 0.10 s. If your friend holds a ruler between your fingers and releases it without warning, how far can you expect the ruler to fall before you catch it, assuming negligible air resistance?

A hammer is thrown upward with a speed of 14 m/s on the surface of planet X where the acceleration due to gravity is 3.5 m/s2 and there is no atmosphere. What is the speed of the hammer after 8.0 s?