Question 1

A ball is allowed to drop from rest. If the upward direction is positive, then after 2 seconds its velocity will be
A) -19.6 m/s.
B) -9.8 m/s.
C) 9.8 m/s.
D) 19.6 m/s.

Accepted Answer

The velocity of the ball after 2 seconds can be calculated using the equation $v = u + at$, where $u$ is the initial velocity (0 m/s, since it is dropped from rest), $a$ is the acceleration due to gravity (-9.8 m/s$^2$, taking downward as negative), and $t$ is the time (2 seconds). Substituting these values, we get $v = 0 + (-9.8 \times 2) = -19.6$ m/s.

Question 2

A man standing on a bridge throws a stone horizontally with a speed of 20 m/s. The stone hits the water below 2.5 s later. The bridge is
A) 44.1 m high.
B) 60.1 m high.
C) 30.6 m high.
D) 20.3 m high.

Accepted Answer

We can use the equation:
y = vi*t + (1/2)*a*t^2
where y is the vertical displacement, vi is the initial vertical velocity (which is 0 m/s since the stone is thrown horizontally), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time of flight (2.5 s).

We want to solve for the height of the bridge, so we need to find the vertical displacement. Since the stone is thrown horizontally, the horizontal displacement is given by:
x = vi*x*t
where vi,x is the initial horizontal velocity (20 m/s) and x is the horizontal distance traveled (which we don't know yet).

We can rearrange this equation to solve for x:
x = vi,x*t
x = 20 m/s * 2.5 s
x = 50 m

Now we can use the vertical displacement equation with our values:
y = vi*t + (1/2)*a*t^2
y = 0 m/s * 2.5 s + (1/2)*(-9.8 m/s^2)*(2.5 s)^2
y = -30.625 m

Since the stone falls below the level of the bridge, the height of the bridge is equal to the absolute value of the vertical displacement:
|y| = 30.625 m

Therefore, the closest answer choice is C) 30.6 m high.

Question 3

The acceleration of a body is given by the slope of a graph plotting
A) distance travelled versus time.
B) time versus velocity.
C) velocity versus distance travelled.
D) velocity versus time.
E) time versus distance travelled.

Accepted Answer

The acceleration of a body is defined as the rate of change of velocity over time. Therefore, the best choice for a graph that represents the acceleration would be a graph that plots velocity versus time. The slope of such a graph would give the rate of change of velocity, which is the acceleration.

Question 4

After 1 second, a ball dropped from rest will have fallen
A) 1.0 m.
B) 2.45 m.
C) 4.9 m.
D) 9.8 m.
E) 19.6 m.

Accepted Answer

The distance an object falls is given by the formula:
distance = (1/2) * acceleration * time^2
For this question, the acceleration is the acceleration due to gravity, which is 9.8 m/s^2 downward. Plugging in time = 1 second, we get:
distance = (1/2) * 9.8 m/s^2 * (1 s)^2 = 4.9 m
Therefore, the ball will have fallen 4.9 meters after 1 second.

Question 5

One day while measuring acceleration with his pulse as a timing source, Galileo became so excited that his pulse rate increased. His results for acceleration that day were probably
A) higher than usual.
B) lower than usual.
C) more accurate than usual.
D) unchanged.

Accepted Answer

Galileo's increased pulse rate likely indicated a higher level of excitement or physical activity, which could potentially affect the accuracy of his measurements. Thus, his results for acceleration that day were probably higher than usual.

Question 6

A ball is thrown across the street. During its flight, the ball's speed is lowest at
A) the beginning of its flight.
B) the end of its flight.
C) the highest point of its flight.
D) the speed is constant throughout the flight.

Accepted Answer

At the highest point of its flight, the vertical component of the ball's velocity is zero, making its speed the lowest since only the horizontal component of velocity remains, assuming air resistance is negligible.

Question 7

A 10 pound iron ball and a 2 pound iron ball are dropped simultaneously from a height of 100 meters. Neglecting air resistance, which ball will reach the ground first?
A) The 10 lb ball
B) The 2 lb ball
C) They will reach the ground at the same time.

Accepted Answer

Both balls will reach the ground at the same time because they experience the same acceleration due to gravity, 9.8 m/s^2. This is known as the principle of equivalence and was first demonstrated by Galileo Galilei in the 16th century. The mass of an object does not affect its acceleration due to gravity, only its weight (which is proportional to mass and the acceleration due to gravity). Therefore, both balls will fall at the same rate and hit the ground simultaneously.

Question 8

A ball rolls off a shelf and hits the floor below 0.25 second later. To find the speed of the ball as it left the shelf, we would need
A) the distance measured along the floor to the point of impact.
B) to repeat the experiment.
C) the height of the table.
D) the weight of the ball.

Accepted Answer

The answer of A ball rolls off a shelf and...

Question 9

During the first 5 seconds after a ball is dropped from rest, how far will it fall?
A) 25 m
B) 61.3 m
C) 122.5 m
D) 245 m
E) 490 m

Accepted Answer

The answer of During the first 5 seconds after a...

Question 10

The motion of a falling object is commonly investigated with the aid of a
A) stethoscope.
B) microscope.
C) kaleidoscope.
D) stroboscope.

Accepted Answer

The stroboscope is used to study the motion of a falling object by flashing light at regular intervals to capture images of the object at different points in time. This allows the observer to analyze the motion and position of the object over time. The other options (stethoscope, microscope, kaleidoscope) do not have any practical application in studying the motion of a falling object.

Question 11

Ball A is thrown upward with a velocity of 19.6 m/s. Two seconds later ball B is thrown upward with a velocity of 9.8 m/s. Which ball is first to return to the thrower's hand?
A) A will arrive first.
B) A and B will arrive at the same time.
C) B will arrive first.

Accepted Answer

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

Question 12

A ball thrown upward reaches its maximum height and then falls back. If air resistance is negligible, its acceleration is
A) less on the way up than on the way down.
B) less on the way down than on the way up.
C) the same up and down but zero at the top.
D) the same at all points in the motion.

Accepted Answer

The acceleration due to gravity is constant throughout the motion of the ball, both upwards and downwards, and does not change even at the maximum height.

Question 13

A ball is projected upward with an initial velocity of 10 m/s. It will reach its maximum height in approximately
A) 1 s.
B) 1.5 s.
C) 2 s.
D) 2.5 s.
E) 3 s.

Accepted Answer

The time to reach maximum height is given by t = v/g, where v is the initial velocity and g is the acceleration due to gravity (approximately 9.8 m/s²). So, t = 10/9.8 ≈ 1 s.

Question 14

Which of the following does not move like a projectile?
A) A monkey jumping from a tree
B) The seeds at a watermelon seed spitting contest
C) An airplane flying at a constant altitude
D) A rock kicked up by a truck wheel

Accepted Answer

An airplane flying at a constant altitude is not moving like a projectile because it is constantly being propelled forward by its engines and is not being acted upon by gravity in the same way as the other objects listed. The other options are all subject to gravity and are launched into the air with a particular trajectory, making them move like projectiles.

Question 15

The acceleration due to gravity near the surface of Mars is about one-third of the value near the Earth's surface. If a rock fell from rest for the same amount of time on Mars and Earth, the final speed of the rock would be
A) three times faster than on Earth.
B) the square root of three times faster than on Earth.
C) the same speed as on Earth.
D) the square root of three times slower than on Earth.
E) three times slower than on Earth.

Accepted Answer

The final speed of an object in free fall is directly proportional to the acceleration due to gravity. Since Mars' gravity is about one-third of Earth's, the final speed on Mars would be three times slower than on Earth for the same fall time.

Question 16

If air resistance can be ignored, which of the following graphs will be a straight line for a falling object?
A) Distance travelled versus time.
B) Distance travelled versus velocity.
C) Time versus distance travelled.
D) Velocity versus time.
E) Velocity versus distance travelled.

Accepted Answer

If air resistance can be ignored, the only force acting on an object in free fall is gravity, which causes a constant acceleration. Therefore, the velocity of the object will change at a constant rate over time, resulting in a straight line on a velocity versus time graph.

Question 17

A ball is thrown straight up with an initial velocity of 10 m/s. After 3 seconds its velocity will be
A) -19.4 m/s.
B) -29.4 m/s.
C) 0 m/s.
D) 29.4 m/s.
E) 19.4 m/s.

Accepted Answer

The velocity of the ball after 3 seconds can be found using the equation $v = u + at$, where $v$ is the final velocity, $u$ is the initial velocity (10 m/s upwards), $a$ is the acceleration due to gravity (-9.8 m/s$^2$ downwards), and $t$ is the time (3 seconds). Substituting the values, we get $v = 10 + (-9.8)(3) = 10 - 29.4 = -19.4$ m/s. The negative sign indicates that the velocity is in the opposite direction of the initial throw, meaning the ball is moving downwards after 3 seconds.

Question 18

The acceleration due to gravity near the surface of the Moon is about one-sixth of the value near the Earth's surface. If a rock were dropped from equal heights on the Moon and Earth, the time it would take the rock from the Moon to hit the ground would be
A) six times longer than on Earth.
B) the square root of six times longer than on Earth.
C) the same time as on Earth.
D) the square root of six times shorter than on Earth.
E) six times shorter than on Earth.

Accepted Answer

The time taken for an object to fall under gravity is proportional to the square root of the inverse of the acceleration due to gravity. Since the Moon's gravity is one-sixth that of Earth's, the time taken on the Moon would be the square root of six times longer than on Earth.

Question 19

A bullet is fired horizontally at a target 20 m away. The velocity of the bullet as it leaves the gun is 200 m/s. How much, approximately, will the bullet drop on its way to the target?
A) 0.05 m
B) 0.1 m
C) 0.2 m
D) 0.3 m
E) 0.4 m

Accepted Answer

The bullet's vertical drop can be calculated using the formula $d = \frac{1}{2}gt^2$, where $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$) and $t$ is the time of flight. The time $t$ can be found from the horizontal motion, given by $t = \frac{d}{v}$, where $d = 20 m$ is the distance to the target and $v = 200 m/s$ is the velocity of the bullet. Thus, $t = \frac{20}{200} = 0.1 s$. Substituting $t = 0.1 s$ into the formula for vertical drop gives $d = \frac{1}{2} \times 9.8 \times (0.1)^2 = 0.049 m$, which is approximately $0.05 m$.

Question 20

Assuming g = 10 m/s² and that air resistance is negligible, in 1/2 second a ball dropped from rest will fall A) 0.3 m. B) 0.8 m. C) 1.0 m. D) 1.25 m. E) 2.25 m.

Accepted Answer

The distance fallen by a freely falling object can be calculated using the formula:
d = (1/2)gt^2
where d is the distance, g is the acceleration due to gravity, and t is the time. Plugging in g = 10 m/s^2 and t = 1/2 s, we get:
d = (1/2)(10)(1/2)^2 = 1.25 m
Therefore, the ball will fall 1.25 meters in 1/2 second. The correct answer is D.

Quiz 3: Falling Objects and Projectile Motion

A ball is allowed to drop from rest. If the upward direction is positive, then after 2 seconds its velocity will be

A man standing on a bridge throws a stone horizontally with a speed of 20 m/s. The stone hits the water below 2.5 s later. The bridge is

The acceleration of a body is given by the slope of a graph plotting

After 1 second, a ball dropped from rest will have fallen

One day while measuring acceleration with his pulse as a timing source, Galileo became so excited that his pulse rate increased. His results for acceleration that day were probably

A ball is thrown across the street. During its flight, the ball's speed is lowest at

A 10 pound iron ball and a 2 pound iron ball are dropped simultaneously from a height of 100 meters. Neglecting air resistance, which ball will reach the ground first?

A ball rolls off a shelf and hits the floor below 0.25 second later. To find the speed of the ball as it left the shelf, we would need

During the first 5 seconds after a ball is dropped from rest, how far will it fall?

The motion of a falling object is commonly investigated with the aid of a

Ball A is thrown upward with a velocity of 19.6 m/s. Two seconds later ball B is thrown upward with a velocity of 9.8 m/s. Which ball is first to return to the thrower's hand?

A ball thrown upward reaches its maximum height and then falls back. If air resistance is negligible, its acceleration is

A ball is projected upward with an initial velocity of 10 m/s. It will reach its maximum height in approximately

Which of the following does not move like a projectile?

The acceleration due to gravity near the surface of Mars is about one-third of the value near the Earth's surface. If a rock fell from rest for the same amount of time on Mars and Earth, the final speed of the rock would be

If air resistance can be ignored, which of the following graphs will be a straight line for a falling object?

A ball is thrown straight up with an initial velocity of 10 m/s. After 3 seconds its velocity will be

The acceleration due to gravity near the surface of the Moon is about one-sixth of the value near the Earth's surface. If a rock were dropped from equal heights on the Moon and Earth, the time it would take the rock from the Moon to hit the ground would be

A bullet is fired horizontally at a target 20 m away. The velocity of the bullet as it leaves the gun is 200 m/s. How much, approximately, will the bullet drop on its way to the target?

Assuming g = 10 m/s2 and that air resistance is negligible, in 1/2 second a ball dropped from rest will fall

Assuming g = 10 m/s² and that air resistance is negligible, in 1/2 second a ball dropped from rest will fall