Question 1

An astronaut stands by the rim of a crater on the moon, where the acceleration of gravity is 1.62 m/s². To determine the depth of the crater, she drops a rock and measures the time it takes for it to hit the bottom. If the time is 6.3 s, what is the depth of the crater? A) 10 m B) 14 m C) 26 m D) 32 m E) 38 m

Accepted Answer

The depth of the crater can be calculated using the formula:$$d = 1/2 * g * t^2$$where:d is the depth of the craterg is the acceleration of gravityt is the time it takes for the rock to hit the bottomPlugging in the given values, we get:$$d = 1/2 * 1.62 m/s^2 * (6.3 s)^2 = 32.4 m$$Therefore, the depth of the crater is 32.4 m, which is closest to choice D) 32 m.

Question 2

An object is thrown upwards with a speed of 14 .0 m/s. How long does it take it to reach its maximum height?
A) 1.22 s
B) 1.43 s
C) 3.14 s
D) 4.15 s
E) 5.31 s

Accepted Answer

To find the time it takes for the object to reach its maximum height, we need to use the formula t = v/ g, where v is the initial velocity and g is the acceleration due to gravity. Since the object is thrown upwards, we take g to be negative (-9.8 m/s^2). Therefore, t = 14.0 / 9.8 = 1.43 s (rounded to two decimal places).

Question 3

To determine the height of a bridge above the water, a person drops a stone and measures the time it takes for it to hit the water. If the height of the bridge is 41 m, how long will it take for the stone to hit the water?
A) 2.3 s
B) 2.6 s
C) 2.9 s
D) 3.2 s
E) 3.6 s

Accepted Answer

The time it takes for an object to fall from a height h is given by the formula t = √(2h/g), where g is the acceleration due to gravity (approximately 9.8 m/s²). Plugging in the values, t = √(2*41/9.8) ≈ 2.9 seconds.

Question 4

An object is thrown upwards with a speed of 13 m/s. How long does it take to reach a height of 4.0 m above the projection point while descending?
A) 0.42 s
B) 1.2 s
C) 2.3 s
D) 3.1 s
E) 4.2 s

Accepted Answer

We can use the kinematic equation:

h = vi*t - 0.5*g*t^2

where h is the height, vi is the initial velocity, g is the acceleration due to gravity (-9.8 m/s^2), and t is time.

Since the object is descending, its initial velocity is negative (-13 m/s). Plugging in the given values and solving for t:

4.0 m = -13 m/s * t - 0.5 * (-9.8 m/s^2) * t^2

t^2 + (13/9.8) * t - 0.816 = 0

Using the quadratic formula (or factoring), we get:

t = 2.3 s (rounding to one decimal place)

Therefore, the object takes 2.3 s to reach a height of 4.0 m above the projection point while descending.

Question 5

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 0.5 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?
A) 10 m
B) 13 m
C) 16 m
D) 18 m
E) 26 m

Accepted Answer

The answer of To determine the height of a flagpole,...

Question 6

An object is dropped from a bridge. A second object is thrown downwards 1.00 s later. They both reach the water 20.0 m below at the same instant. What was the initial speed of the second object?
A) 4.91 m/s
B) 14.6 m/s
C) 9.90 m/s
D) 19.6 m/s
E) 21.3 m/s

Accepted Answer

The answer of An object is dropped from a bridge....

Question 7

An object is thrown upwards with a speed of 16 m/s. How long does it take it to reach a height of 7.0 m on the way up?
A) 0.52 s
B) 1.2 s
C) 2.4 s
D) 3.1 s
E) 4.2 s

Accepted Answer

Using the kinematic equation $ h = v_i t - \frac{1}{2} g t^2 $, where $ h = 7.0 \, \text{m} $, $ v_i = 16 \, \text{m/s} $, and $ g = 9.8 \, \text{m/s}^2 $, solving for $ t $ gives approximately 0.52 s.

Question 8

Abby throws a ball straight up and times it. She sees that the ball goes by the top of a flagpole after 0.500 s and reaches the level of the top of the pole after a total elapsed time of 4.10 s. What was the speed of the ball at launch?
A) 11.3 m/s
B) 22.6 m/s
C) 33.9 m/s
D) 45.2 m/s
E) 48.3 m/s

Accepted Answer

The ball takes 0.500 s to reach the top of the flagpole and 4.10 s to return to the same level. The total time for the upward journey is half of 4.10 s, which is 2.05 s. Using the equation for motion under gravity, v = u + at, where v = 0 m/s at the top, a = -9.8 m/s², and t = 2.05 s, we solve for u (initial velocity) to find u = 22.6 m/s.

Question 9

Abby throws a ball straight up and times it. She sees that the ball goes by the top of a flagpole after 0.50 s and reaches the level of the top of the pole after a total elapsed time of 4.10 s. What was the speed of the ball at as it passed the top of the flagpole?
A) 6.40 m/s
B) 16.2 m/s
C) 17.6 m/s
D) 29.0 m/s
E) 33 m/s

Accepted Answer

The ball takes 0.50 s to reach the top of the flagpole and 3.60 s (4.10 s - 0.50 s) to return to the same level. Using the symmetry of projectile motion and the formula v = u + at, where a = -9.8 m/s², the initial speed u can be calculated as 17.6 m/s.

Question 10

To determine the height of a bridge above the water, a person drops a stone and measures the time it takes for it to hit the water. If the time is 2.3 s, what is the height of the bridge?
A) 10 m
B) 14 m
C) 26 m
D) 32 m
E) 52 m

Accepted Answer

The height of the bridge can be determined using the formula:

h = (1/2)gt^2

where h is the height, g is the acceleration due to gravity (9.81 m/s^2), and t is the time taken.

Plugging in the given values, we have:

h = (1/2) × 9.81 m/s^2 × (2.3 s)^2
h = 26.05 m

Rounding off to the nearest meter, we get the answer as 26 m.

Question 11

An object is thrown upwards with a speed of 14 m/s. How high above the projection point is it after 0.50 s?
A) 0 m
B) 2.9 m
C) 5.8 m
D) 7.0 m
E) 8.2 m

Accepted Answer

Using the kinematic equation, 
y = y0 + v0t + 0.5at^2
where y is the final height, y0 is the initial height (0 in this case), v0 is the initial velocity (14 m/s), t is the time (0.5 s), and a is the acceleration due to gravity (-9.8 m/s^2). 
Plugging in the values, we get 
y = 0 + (14 m/s)(0.5 s) + 0.5(-9.8 m/s^2)(0.5 s)^2 
y = 5.8 m 
Therefore, the object is 5.8 meters above the projection point after 0.50 seconds. 
The correct answer is option C.

Question 12

An astronaut stands by the rim of a crater on the moon, where the acceleration of gravity is 1.62 m/s² To determine the depth of the crater, she drops a rock and measures the time it takes for it to hit the bottom. If the depth of the crater is 120 m, how long does it take for the rock to fall? A) 3.04 s B) 12.2 s C) 29.3 s D) 32.1 s E) 37.5 s

Accepted Answer

The answer of An astronaut stands by the rim of...

Quiz 2: One-Dimensional Kinematics

An astronaut stands by the rim of a crater on the moon, where the acceleration of gravity is 1.62 m/s2. To determine the depth of the crater, she drops a rock and measures the time it takes for it to hit the bottom. If the time is 6.3 s, what is the depth of the crater?

An object is thrown upwards with a speed of 14 .0 m/s. How long does it take it to reach its maximum height?

To determine the height of a bridge above the water, a person drops a stone and measures the time it takes for it to hit the water. If the height of the bridge is 41 m, how long will it take for the stone to hit the water?

An object is thrown upwards with a speed of 13 m/s. How long does it take to reach a height of 4.0 m above the projection point while descending?

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 0.5 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?

An object is dropped from a bridge. A second object is thrown downwards 1.00 s later. They both reach the water 20.0 m below at the same instant. What was the initial speed of the second object?

An object is thrown upwards with a speed of 16 m/s. How long does it take it to reach a height of 7.0 m on the way up?

Abby throws a ball straight up and times it. She sees that the ball goes by the top of a flagpole after 0.500 s and reaches the level of the top of the pole after a total elapsed time of 4.10 s. What was the speed of the ball at launch?

Abby throws a ball straight up and times it. She sees that the ball goes by the top of a flagpole after 0.50 s and reaches the level of the top of the pole after a total elapsed time of 4.10 s. What was the speed of the ball at as it passed the top of the flagpole?

To determine the height of a bridge above the water, a person drops a stone and measures the time it takes for it to hit the water. If the time is 2.3 s, what is the height of the bridge?

An object is thrown upwards with a speed of 14 m/s. How high above the projection point is it after 0.50 s?

An astronaut stands by the rim of a crater on the moon, where the acceleration of gravity is 1.62 m/s2 To determine the depth of the crater, she drops a rock and measures the time it takes for it to hit the bottom. If the depth of the crater is 120 m, how long does it take for the rock to fall?

An astronaut stands by the rim of a crater on the moon, where the acceleration of gravity is 1.62 m/s². To determine the depth of the crater, she drops a rock and measures the time it takes for it to hit the bottom. If the time is 6.3 s, what is the depth of the crater?

An astronaut stands by the rim of a crater on the moon, where the acceleration of gravity is 1.62 m/s² To determine the depth of the crater, she drops a rock and measures the time it takes for it to hit the bottom. If the depth of the crater is 120 m, how long does it take for the rock to fall?