Question 1

A rock is dropped from the top of a vertical cliff and takes 3.00 s to reach the ground below the cliff. A second rock is thrown vertically from the cliff, and it takes this rock 2.00 s to reach the ground below the cliff from the time it is released. With what velocity was the second rock thrown, assuming no air resistance?

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Question 2

A toy rocket is launched vertically from ground level (y = 0.00 m), 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 72 m and acquired a velocity of  The rocket continues to rise in unpowered flight, reaches maximum height, and falls back to the ground with negligible air resistance. The speed of the rocket upon impact on the ground is closest to

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Question 3

Two identical stones are dropped from rest and feel no air resistance as they fall. Stone A is dropped from height h, and stone B is dropped from height 2h. If stone A takes time t to reach the ground, stone B will take time

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Question 4

A speeding car is traveling at a constant 30.0 m/s when it passes a stationary police car. If the police car delays for 1.00 s before starting, what must be the magnitude of the constant acceleration of the police car to catch the speeding car after the police car travels a distance of 300 m?

Accepted Answer

First, we can find the time it takes for the police car to catch up to the speeding car assuming they both start at the same time. This can be found using the equation:
distance = rate x time
We know the distance is 300 m and the rate is the same for both cars (30 m/s), so:
300 m = 30 m/s x time
time = 10 s
Now we can find how far the speeding car travels in the 1 second delay of the police car:
distance = rate x time
distance = 30 m/s x 1 s
distance = 30 m
So, when the police car starts moving, the speeding car is 30 m ahead of them.
To catch up, the police car needs to cover this distance (30 m) and the original 300 m in the same amount of time (10 s). So we can use the equation:
distance = 1/2 x acceleration x time^2 + initial velocity x time
where the initial velocity for the police car is 0 m/s. Plugging in:
330 m = 1/2 x acceleration x (10 s)^2
solving for acceleration:
acceleration = 6.60 m/s^2
which is closest to choice C, 7.41 m/s^2.

Question 5

A foul ball is hit straight up into the air with a speed of 30.0 m/s.
(a) Calculate the time required for the ball to rise to its maximum height.
(b) Calculate the maximum height reached by the ball.
(c) Determine the time at which the ball pass a point 25.0 m above the point of contact between the bat and ball.
(d) Explain why there are two answers to part (c).

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Question 6

At the same moment from the top of a building 3.0 × 10² m tall, one rock is dropped and one is thrown downward with an initial velocity of . Both of them experience negligible air resistance. How much EARLIER does the thrown rock strike the ground?

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Question 7

A car is 200 m from a stop sign and traveling toward the sign at 40.0 m/s. At this time, the driver suddenly realizes that she must stop the car. If it takes 0.200 s for the driver to apply the brakes, what must be the magnitude of the constant acceleration of the car after the brakes are applied so that the car will come to rest at the stop sign?

Accepted Answer

First, we need to find how far the car will travel during the driver's reaction time of 0.200 s. Using the equation $d = vt$, we get:

$d = (40.0 	ext{ m/s})(0.200 	ext{ s}) = 8.00 	ext{ m}$

This means that when the driver applies the brakes, the car is 200 m - 8.00 m = 192 m away from the stop sign.

Now, using the equation $v_f^2 = v_i^2 + 2ad$, we can solve for the acceleration needed to bring the car to a stop:

$0 = (40.0 	ext{ m/s})^2 + 2a(192 	ext{ m})$

$a = -{40.0^2 \over 2(192)} = -41.7 	ext{ m/s}^2$

Note that the acceleration is negative because it is in the opposite direction of the car's motion. Taking the magnitude, we get:

$|a| = 41.7 	ext{ m/s}^2 \approx \boxed{	extbf{(C) }4.17 	ext{ m/s}^2}$

Question 8

A package is dropped from a helicopter moving upward at  If it takes  before the package strikes the ground, how high above the ground was the package when it was released if air resistance is negligible?

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Question 9

A ball is projected upward at time t = 0.00 s, from a point on a roof 70 m above the ground and experiences negligible air resistance. The ball rises, then falls and strikes the ground. The initial velocity of the ball is  Consider all quantities as positive in the upward direction. The velocity of the ball when it is  above the ground is closest to

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Question 10

A ball rolls across a floor with an acceleration of 0.100 m/s² in a direction opposite to its velocity. The ball has a velocity of 4.00 m/s after rolling a distance 6.00 m across the floor. What was the initial speed of the ball?

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Question 11

To determine the height of a flagpole, Abby throws a ball straight up and times it. She sees that the ball goes by the top of the pole after 0.50 s and then reaches the top of the pole again after a total elapsed time of 4.1 s. How high is the pole above the point where the ball was launched? (You can ignore air resistance.)

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Question 12

Two identical objects A and B fall from rest from different heights to the ground and feel no appreciable air resistance. If object B takes TWICE as long as object A to reach the ground, what is the ratio of the heights from which A and B fell?

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Question 13

A soccer ball is released from rest at the top of a grassy incline. After 8.6 seconds, the ball travels 87 meters and 1.0 s after this, the ball reaches the bottom of the incline.
(a) What was the magnitude of the ball's acceleration, assume it to be constant?
(b) How long was the incline?

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The answer of A soccer ball is released from rest...

Question 14

A car starts from rest and accelerates with a constant acceleration of 1.00 m/s² for 3.00 s. The car continues for 5.00 s at constant velocity. How far has the car traveled from its starting point?

Accepted Answer

The distance traveled during the first 3.00 s of constant acceleration is given by:

$d = \frac{1}{2}at^2 = \frac{1}{2}(1.00	ext{ m/s}^2)(3.00	ext{ s})^2 = 4.50	ext{ m}$

During the next 5.00 s of constant velocity, the car travels:

$d = vt = (1.00	ext{ m/s})(5.00	ext{ s}) = 5.00	ext{ m}$

So the total distance traveled is:

$d_{	ext{total}} = 4.50	ext{ m} + 5.00	ext{ m} = 9.50	ext{ m}$

The closest answer choice to this value is C, 19.5 m, which is within the range (9.25 m to 9.75 m) of possible values. Therefore, the correct answer is C.

Question 15

On the earth, when an astronaut throws a 0.250-kg stone vertically upward, it returns to his hand a time T later. On planet X he finds that, under the same circumstances, the stone returns to his hand in 2T. In both cases, he throws the stone with the same initial velocity and it feels negligible air resistance. The acceleration due to gravity on planet X (in terms of g) is

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Question 16

A rock is thrown directly upward from the edge of the roof of a building that is 66.2 meters tall. The rock misses the building on its way down, and is observed to strike the ground 4.00 seconds after being thrown. Neglect any effects of air resistance. With what speed was the rock thrown?

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Question 17

A rocket takes off vertically from the launchpad with no initial velocity but a constant upward acceleration of 2.25 m/s². At 15.4 s after blastoff, the engines fail completely so the only force on the rocket from then on is the pull of gravity. (a) What is the maximum height the rocket will reach above the launchpad? (b) How fast is the rocket moving at the instant before it crashes onto the launchpad? (c) How long after engine failure does it take for the rocket to crash onto the launchpad?

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Question 18

A test rocket is fired straight up from rest with a net acceleration of 20.0 m/s². After 4.00 seconds the motor turns off, but the rocket continues to coast upward with no appreciable air resistance. What maximum elevation does the rocket reach?

Accepted Answer

To find the maximum elevation, we first calculate the distance traveled during the powered phase and then add the distance it coasts upward after the motor turns off. 1. During the powered phase (first 4 seconds), we use the equation $d = \frac{1}{2}at^2$, where $a = 20.0 \, m/s^2$ and $t = 4.0 \, s$. This gives us $d = \frac{1}{2} \times 20.0 \times (4.0)^2 = 160 \, m$.2. To find the velocity at the end of the powered phase, we use $v = at$, giving us $v = 20.0 \times 4.0 = 80.0 \, m/s$.3. For the coasting phase, we use the equation for motion under gravity $v^2 = u^2 + 2as$, where $v = 0$ (at the maximum height), $u = 80.0 \, m/s$, $a = -9.8 \, m/s^2$ (acceleration due to gravity acting downwards), and $s$ is the distance. Rearranging for $s$, we get $s = \frac{u^2}{2g} = \frac{(80.0)^2}{2 \times 9.8} \approx 327 \, m$.4. The total elevation is the sum of the distances in the powered and coasting phases: $160 \, m + 327 \, m = 487 \, m$.Therefore, the maximum elevation reached by the rocket is 487 meters.

Question 19

A ball is projected upward at time t = 0.0 s, from a point on a roof 90 m above the ground. The ball rises, then falls and strikes the ground. The initial velocity of the ball is  if air resistance is negligible. The time when the ball strikes the ground is closest to

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Quiz 2: Kinematics in One Dimension

Two identical stones are dropped from rest and feel no air resistance as they fall. Stone A is dropped from height h, and stone B is dropped from height 2h. If stone A takes time t to reach the ground, stone B will take time

A speeding car is traveling at a constant 30.0 m/s when it passes a stationary police car. If the police car delays for 1.00 s before starting, what must be the magnitude of the constant acceleration of the police car to catch the speeding car after the police car travels a distance of 300 m?

At the same moment from the top of a building 3.0 × 102 m tall, one rock is dropped and one is thrown downward with an initial velocity of . Both of them experience negligible air resistance. How much EARLIER does the thrown rock strike the ground?

A package is dropped from a helicopter moving upward at If it takes before the package strikes the ground, how high above the ground was the package when it was released if air resistance is negligible?

A ball rolls across a floor with an acceleration of 0.100 m/s2 in a direction opposite to its velocity. The ball has a velocity of 4.00 m/s after rolling a distance 6.00 m across the floor. What was the initial speed of the ball?

Two identical objects A and B fall from rest from different heights to the ground and feel no appreciable air resistance. If object B takes TWICE as long as object A to reach the ground, what is the ratio of the heights from which A and B fell?

A soccer ball is released from rest at the top of a grassy incline. After 8.6 seconds, the ball travels 87 meters and 1.0 s after this, the ball reaches the bottom of the incline. (a) What was the magnitude of the ball's acceleration, assume it to be constant? (b) How long was the incline?

A car starts from rest and accelerates with a constant acceleration of 1.00 m/s2 for 3.00 s. The car continues for 5.00 s at constant velocity. How far has the car traveled from its starting point?

A rock is thrown directly upward from the edge of the roof of a building that is 66.2 meters tall. The rock misses the building on its way down, and is observed to strike the ground 4.00 seconds after being thrown. Neglect any effects of air resistance. With what speed was the rock thrown?

A test rocket is fired straight up from rest with a net acceleration of 20.0 m/s2. After 4.00 seconds the motor turns off, but the rocket continues to coast upward with no appreciable air resistance. What maximum elevation does the rocket reach?

A ball is projected upward at time t = 0.0 s, from a point on a roof 90 m above the ground. The ball rises, then falls and strikes the ground. The initial velocity of the ball is if air resistance is negligible. The time when the ball strikes the ground is closest to

At the same moment from the top of a building 3.0 × 10² m tall, one rock is dropped and one is thrown downward with an initial velocity of . Both of them experience negligible air resistance. How much EARLIER does the thrown rock strike the ground?

A ball rolls across a floor with an acceleration of 0.100 m/s² in a direction opposite to its velocity. The ball has a velocity of 4.00 m/s after rolling a distance 6.00 m across the floor. What was the initial speed of the ball?

A car starts from rest and accelerates with a constant acceleration of 1.00 m/s² for 3.00 s. The car continues for 5.00 s at constant velocity. How far has the car traveled from its starting point?

A test rocket is fired straight up from rest with a net acceleration of 20.0 m/s². After 4.00 seconds the motor turns off, but the rocket continues to coast upward with no appreciable air resistance. What maximum elevation does the rocket reach?