Question 1

A toy rocket,launched from the ground,rises vertically with an acceleration of 20 m/s² for 6.0 s until its motor stops.Disregarding any air resistance,what maximum height above the ground will the rocket achieve? A)1.1 km B)0.73 km C)1.9 km D)0.39 km E)1.5 km

Accepted Answer

The answer of A toy rocket,launched from the ground,rises vertically...

Question 2

The velocity at the midway point of a ball able to reach a height y when thrown with velocity v_i at the origin is: A) $\frac { v _ { i } } { 2 }$ B) $\sqrt { v _ { i } ^ { 2 } 2 g y }$ C) $\sqrt { \frac { v _ { i } ^ { 2 } } { 2 } }$ D) $\sqrt { v _ { i } ^ { 2 } + 2 g y }$ E)gy

Accepted Answer

At the midway point, the kinetic energy is half of the initial kinetic energy, so the velocity is $\sqrt{\frac{v_i^2}{2}}$.

Question 3

A peregrine falcon dives at a pigeon.The falcon starts with zero downward velocity and falls with the acceleration of gravity.If the pigeon is 76.0 m below the initial height of the falcon,how long does it take the falcon to intercept the pigeon?

Accepted Answer

The answer of A peregrine falcon dives at a pigeon.The...

Question 4

The equation that solves a problem is $$6.4 \mathrm {~m} = 20 \mathrm {~m} + 3.0 \frac { \mathrm { m } } { \mathrm { s } } ( 2.0 \mathrm {~s} ) - 4.9 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } } ( 2.0 \mathrm {~s} ) ^ { 2 }$$ .The problem is:
A)How far above its initial position does a rock travel in 2.0 s when thrown up from a point 40 m above the ground?
B)How far below its initial position does a rock travel in 2.0 s when thrown up from a point 40 m above the ground?
C)What is the position relative to the ground of a rock thrown up at 3.0 m/s from a roof 20 m above the ground 2.0 s after it is released?
D)What is the change in position relative to the ground of a rock thrown up at 3.0 m/s from a roof 20 m above the ground 2.0 s after it is released?
E)What is the position relative to the ground of a rock thrown up at 3.0 m/s from a roof 20 m above the ground if its maximum height is 33.6 m?

Accepted Answer

The equation given in the problem is the equation for vertical displacement of an object (in this case, a rock) thrown upwards with an initial velocity of 3.0 m/s from a height of 40 m above ground level.

To solve for the position of the rock relative to the ground 2.0 s after it is released, we can simply substitute the values given in the problem into the equation and solve for the vertical displacement.

$$6.4 \mathrm {~m} = 20 \mathrm {~m} + 3.0 \frac { \mathrm { m } } { \mathrm { s } } ( 2.0 \mathrm {~s} ) - 4.9 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } } ( 2.0 \mathrm {~s} ) ^ { 2 }$$

$$6.4 \mathrm {~m} = 20 \mathrm {~m} + 6.0 \mathrm {~m} - 19.6 \mathrm {~m}$$

$$6.4 \mathrm {~m} = 6.4 \mathrm {~m}$$

Therefore, the position of the rock relative to the ground 2.0 s after it is released is 6.4 m above the ground.

Question 5

A car originally traveling at 30 m/s manages to brake for 5.0 seconds while traveling 125 m downhill.At that point the brakes fail.After an additional 5.0 seconds it travels an additional 150 m down the hill.What was the acceleration of the car after the brakes failed?

Accepted Answer

The answer of A car originally traveling at 30 m/s...

Question 6

Starting from rest,a car travels 1 350 meters in 1.00 minute.It accelerated at 1.0 m/s² until it reached its cruising speed.Then it drove the remaining distance at constant velocity.What was its cruising speed?

Accepted Answer

The answer of Starting from rest,a car travels 1 350...

Question 7

A bicyclist starts down a hill with an initial speed of 2.0 m/s.She moves down the hill with a constant acceleration,arriving at the bottom of the hill with a speed of 8.0 m/s.If the hill is 12 m long,how long did it take the bicyclist to travel down the hill?

Accepted Answer

The answer of A bicyclist starts down a hill with...

Question 8

Two identical balls are at rest side by side at the bottom of a hill.Some time after ball A is kicked up the hill,ball B is given a kick up the hill.Ball A is headed downhill when it passes ball B headed up the hill.At the instant when ball A passes ball B,
A)it has the same position and velocity as ball B.
B)it has the same position and acceleration as ball B.
C)it has the same velocity and acceleration as ball B.
D)it has the same displacement and velocity as ball B.
E)it has the same position,displacement and velocity as ball B.

Accepted Answer

At the instant when ball A passes ball B, both balls are at the same position on the hill, and since they are on the same slope, they experience the same acceleration due to gravity. However, their velocities are different because they are moving in opposite directions.

Question 9

A 50-gram superball traveling at 25.0 m/s is bounced off a brick wall and rebounds at 22.0 m/s.A high-speed camera records this event.If the ball is in contact with the wall for 3.50 ms,what is the average acceleration of the ball during this time interval?

Accepted Answer

The answer of A 50-gram superball traveling at 25.0 m/s...

Question 10

A ball thrown vertically from ground level is caught 3.0 s later when it is at its highest point by a person on a balcony which is 14 m above the ground.Determine the initial speed of the ball.
A)19 m/s
B)4.7 m/s
C)10 m/s
D)34 m/s
E)17 m/s

Accepted Answer

The ball reaches its highest point in 3.0 s, which means it took 1.5 s to reach the maximum height (since the time to go up equals the time to come down in projectile motion). Using the formula $v = u + at$ for vertical motion (where $v$ is the final velocity, $u$ is the initial velocity, $a$ is the acceleration due to gravity (-9.8 m/s$^2$), and $t$ is the time), and knowing that at the highest point the final velocity ($v$) is 0 m/s, we can rearrange the formula to solve for $u$: $u = v - at$. Substituting $v = 0$, $a = -9.8$ m/s$^2$ (taking upward direction as positive), and $t = 1.5$ s, we get $u = 0 - (-9.8 \times 1.5) = 14.7$ m/s. However, this initial speed is only for the vertical component to reach the balcony. To find the total initial speed to reach the balcony at 14 m in 3.0 s, we use the formula for the displacement in the vertical direction: $s = ut + \frac{1}{2}at^2$, where $s$ is the displacement (14 m), $u$ is the initial velocity we're trying to find, $a$ is the acceleration due to gravity (-9.8 m/s$^2$), and $t$ is the time (3.0 s). Rearranging and solving for $u$ gives us the initial speed required to reach 14 m in height over 3.0 s, which correctly matches the scenario described. The calculation provided initially was incorrect in the context of the question's specifics, leading to confusion. The correct approach involves understanding that the total time of flight is given and the height at which the ball is caught. Given these conditions, the initial speed can be found using kinematic equations that relate time, acceleration, and displacement. The correct initial speed, considering the time to reach the highest point and the height of the balcony, aligns with the principles of projectile motion, where the initial speed required to reach a certain height in a given time can be calculated. My explanation mistakenly mixed concepts and did not accurately apply the correct kinematic equation for this scenario. The correct calculation involves using the given height and time to determine the initial velocity needed to reach that height in the specified time, considering the acceleration due to gravity.

Question 11

A speedy tortoise can run with a velocity of 10.0 cm/s and a hare can run 20.0 times as fast.In a race,they both start at the same time,but the hare stops to rest for 2.00 minutes.The tortoise wins by a shell (20.0 cm).What was the length of the race?

Accepted Answer

The answer of A speedy tortoise can run with a...

Question 12

An object is thrown vertically upward such that it has a speed of 25 m/s when it reaches two thirds of its maximum height above the launch point.Determine this maximum height.
A)64 m
B)48 m
C)32 m
D)96 m
E)75 m

Accepted Answer

The answer of An object is thrown vertically upward such...

Question 13

A rock is thrown downward from an unknown height above the ground with an initial speed of 10 m/s.It strikes the ground 3.0 s later.Determine the initial height of the rock above the ground.
A)44 m
B)14 m
C)74 m
D)30 m
E)60 m

Accepted Answer

Using the formula $h=h_0+v_{0}t+\frac{1}{2}at^{2}$, we can find the initial height of the rock.
Since the rock is thrown downward, its initial velocity is negative. Also, the final height of the rock is equal to zero since it has struck the ground.
Therefore, we have:
$0=h_0-10t+\frac{1}{2}(9.8)t^{2}$
Substituting $t=3.0$, we get:
$0=h_0-30+44.1$
$h_0=74.1$ m
Therefore, the initial height of the rock above the ground is 74.1 m, which is closest to choice (C).

Question 14

A helicopter descends from a height of 600 m with uniform negative acceleration,reaching the ground at rest in 5.00 minutes.Determine the acceleration of the helicopter and its initial velocity.

Accepted Answer

The answer of A helicopter descends from a height of...

Question 15

An object is thrown downward with an initial (t = 0)speed of 10 m/s from a height of 60 m above the ground.At the same instant (t = 0),a second object is propelled vertically upward from ground level with a speed of 40 m/s.At what height above the ground will the two objects pass each other?
A)53 m
B)41 m
C)57 m
D)46 m
E)37 m

Accepted Answer

The answer of An object is thrown downward with an...

Quiz 2: Motion in One Dimension

A toy rocket,launched from the ground,rises vertically with an acceleration of 20 m/s² for 6.0 s until its motor stops.Disregarding any air resistance,what maximum height above the ground will the rocket achieve?

The velocity at the midway point of a ball able to reach a height y when thrown with velocity v_i at the origin is:

A peregrine falcon dives at a pigeon.The falcon starts with zero downward velocity and falls with the acceleration of gravity.If the pigeon is 76.0 m below the initial height of the falcon,how long does it take the falcon to intercept the pigeon?

The equation that solves a problem is $6.4 \mathrm {~m} = 20 \mathrm {~m} + 3.0 \frac { \mathrm { m } } { \mathrm { s } } ( 2.0 \mathrm {~s} ) - 4.9 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } } ( 2.0 \mathrm {~s} ) ^ { 2 }$ .The problem is:

A car originally traveling at 30 m/s manages to brake for 5.0 seconds while traveling 125 m downhill.At that point the brakes fail.After an additional 5.0 seconds it travels an additional 150 m down the hill.What was the acceleration of the car after the brakes failed?

Starting from rest,a car travels 1 350 meters in 1.00 minute.It accelerated at 1.0 m/s² until it reached its cruising speed.Then it drove the remaining distance at constant velocity.What was its cruising speed?

A bicyclist starts down a hill with an initial speed of 2.0 m/s.She moves down the hill with a constant acceleration,arriving at the bottom of the hill with a speed of 8.0 m/s.If the hill is 12 m long,how long did it take the bicyclist to travel down the hill?

Two identical balls are at rest side by side at the bottom of a hill.Some time after ball A is kicked up the hill,ball B is given a kick up the hill.Ball A is headed downhill when it passes ball B headed up the hill.At the instant when ball A passes ball B,

A 50-gram superball traveling at 25.0 m/s is bounced off a brick wall and rebounds at 22.0 m/s.A high-speed camera records this event.If the ball is in contact with the wall for 3.50 ms,what is the average acceleration of the ball during this time interval?

A ball thrown vertically from ground level is caught 3.0 s later when it is at its highest point by a person on a balcony which is 14 m above the ground.Determine the initial speed of the ball.

A speedy tortoise can run with a velocity of 10.0 cm/s and a hare can run 20.0 times as fast.In a race,they both start at the same time,but the hare stops to rest for 2.00 minutes.The tortoise wins by a shell (20.0 cm).What was the length of the race?

An object is thrown vertically upward such that it has a speed of 25 m/s when it reaches two thirds of its maximum height above the launch point.Determine this maximum height.

A rock is thrown downward from an unknown height above the ground with an initial speed of 10 m/s.It strikes the ground 3.0 s later.Determine the initial height of the rock above the ground.

A helicopter descends from a height of 600 m with uniform negative acceleration,reaching the ground at rest in 5.00 minutes.Determine the acceleration of the helicopter and its initial velocity.

An object is thrown downward with an initial (t = 0) speed of 10 m/s from a height of 60 m above the ground.At the same instant (t = 0) ,a second object is propelled vertically upward from ground level with a speed of 40 m/s.At what height above the ground will the two objects pass each other?

Quiz 2: Motion in One Dimension

A toy rocket,launched from the ground,rises vertically with an acceleration of 20 m/s2 for 6.0 s until its motor stops.Disregarding any air resistance,what maximum height above the ground will the rocket achieve?

The velocity at the midway point of a ball able to reach a height y when thrown with velocity vi at the origin is:

A peregrine falcon dives at a pigeon.The falcon starts with zero downward velocity and falls with the acceleration of gravity.If the pigeon is 76.0 m below the initial height of the falcon,how long does it take the falcon to intercept the pigeon?

A car originally traveling at 30 m/s manages to brake for 5.0 seconds while traveling 125 m downhill.At that point the brakes fail.After an additional 5.0 seconds it travels an additional 150 m down the hill.What was the acceleration of the car after the brakes failed?

Starting from rest,a car travels 1 350 meters in 1.00 minute.It accelerated at 1.0 m/s2 until it reached its cruising speed.Then it drove the remaining distance at constant velocity.What was its cruising speed?

A bicyclist starts down a hill with an initial speed of 2.0 m/s.She moves down the hill with a constant acceleration,arriving at the bottom of the hill with a speed of 8.0 m/s.If the hill is 12 m long,how long did it take the bicyclist to travel down the hill?

Two identical balls are at rest side by side at the bottom of a hill.Some time after ball A is kicked up the hill,ball B is given a kick up the hill.Ball A is headed downhill when it passes ball B headed up the hill.At the instant when ball A passes ball B,

A 50-gram superball traveling at 25.0 m/s is bounced off a brick wall and rebounds at 22.0 m/s.A high-speed camera records this event.If the ball is in contact with the wall for 3.50 ms,what is the average acceleration of the ball during this time interval?

A ball thrown vertically from ground level is caught 3.0 s later when it is at its highest point by a person on a balcony which is 14 m above the ground.Determine the initial speed of the ball.

A speedy tortoise can run with a velocity of 10.0 cm/s and a hare can run 20.0 times as fast.In a race,they both start at the same time,but the hare stops to rest for 2.00 minutes.The tortoise wins by a shell (20.0 cm).What was the length of the race?

An object is thrown vertically upward such that it has a speed of 25 m/s when it reaches two thirds of its maximum height above the launch point.Determine this maximum height.

A rock is thrown downward from an unknown height above the ground with an initial speed of 10 m/s.It strikes the ground 3.0 s later.Determine the initial height of the rock above the ground.

A helicopter descends from a height of 600 m with uniform negative acceleration,reaching the ground at rest in 5.00 minutes.Determine the acceleration of the helicopter and its initial velocity.

An object is thrown downward with an initial (t = 0) speed of 10 m/s from a height of 60 m above the ground.At the same instant (t = 0) ,a second object is propelled vertically upward from ground level with a speed of 40 m/s.At what height above the ground will the two objects pass each other?

A toy rocket,launched from the ground,rises vertically with an acceleration of 20 m/s² for 6.0 s until its motor stops.Disregarding any air resistance,what maximum height above the ground will the rocket achieve?

The velocity at the midway point of a ball able to reach a height y when thrown with velocity v_i at the origin is:

Starting from rest,a car travels 1 350 meters in 1.00 minute.It accelerated at 1.0 m/s² until it reached its cruising speed.Then it drove the remaining distance at constant velocity.What was its cruising speed?