# Worksheet: Acceleration due to Gravity

In this worksheet, we will practice calculating the properties of the motion of an object that moves under constant acceleration due to gravity.

**Q1: **

A rescue helicopter is hovering over a person whose boat has sunk. One of the rescuers throws a life preserver straight down to the victim with an initial vertically downward velocity of 1.40 m/s and observes that it takes 1.80 s to reach the water. How high above the water was the preserver released?

**Q3: **

Suppose that a person takes 0.35 s
to react and move his hand to catch an object he has dropped. Assume that acceleration
due to gravity on Earth is 9.8 m/s^{2}.

How far does the object fall on Earth?

How far does the object fall on the Moon, where the acceleration due to gravity is one sixth of that on Earth?

**Q5: **

Standing at the base of one of the cliffs of Mt. Arapiles in Victoria, Australia, a 1.60-m tall hiker hears a rock break loose directly overhead. The rock breaks loose 132 m above the ground. The hiker sees the rock 1.10 s after it breaks away.

How far above the hiker is the rock when he sees it?

How much time does he have to move before the rock hits his head?

**Q10: **

A steel ball is dropped onto a hard floor from a height of 2.10 m. The ball rebounds to a height of 1.33 m.

Calculate the magnitude of the velocity of the ball as it strikes the floor.

Calculate the magnitude of the velocity resulting from the rebound.

The ball is in contact with the floor for s. What was the magnitude of the ball’s acceleration during contact with the floor?

- A
m/s
^{2} - B
m/s
^{2} - C
m/s
^{2} - D
m/s
^{2} - E
m/s
^{2}

**Q11: **

A coin is dropped from a hot-air balloon that is 356 m above the ground and rising at 12.3 m/s vertically upward. Assume that vertically upward displacement corresponds to positive values.

Find the distance between the coin and the ground 3.07 s after being released.

Find the velocity of the coin 3.07 s after being released.

Find the time before the coin hits the ground.

**Q13: **

A diver bounces straight up from a diving board, avoiding the diving board on the way down, and falls feet first into a pool. She starts with a velocity of 4.00 m/s and her takeoff point is 1.80 m above the pool.

What is her highest point above the board?

How long a time are her feet in the air?

What is her velocity when her feet hit the water?

**Q14: **

A climber throws a rock into the sky from the top of a cliff, releasing the rock at a point . The rock has an initial vertical velocity of 9.71 m/s, where positive velocity corresponds to vertically upward motion. It takes 2.72 s for the rock to hit the ground at the bottom of the cliff.

Calculate the vertical displacement of the rock from to the point where it hits the ground.

How long would it take for the rock to reach the ground if it is thrown, from , with an initial vertical velocity of m/s?

**Q15: **

A rock is thrown vertically downward with an initial speed of 14.0 m/s from the Verrazano Narrows Bridge in New York City. The roadway of this bridge is 70.0 m above the water. Consider vertically upward displacement as positive-valued.

Calculate the rock’s displacement 0.500 s after release.

Calculate the rock’s displacement 1.00 s after release.

Calculate the rock’s displacement 1.50 s after release.

Calculate the rock’s displacement 2.00 s after release.

Calculate the rock’s displacement 2.50 s after release.

Calculate the rock’s velocity 0.500 s after release.

Calculate the rock’s velocity 1.00 s after release.

Calculate the rock’s velocity 1.50 s after release.

Calculate the rock’s velocity 2.00 s after release.

Calculate the rock’s velocity 2.50 s after release.

**Q17: **

A ball is thrown vertically upward with an initial velocity of 18.5 m/s. The point of release is the position . Take displacements from the release position. Assume upward displacement corresponds to positive values.

What is the displacement of the ball at ?

What is the displacement of the ball at ?

What is the displacement of the ball at ?

What is the displacement of the ball at ?

What is the velocity of the ball at ?

What is the velocity of the ball at ?

What is the velocity of the ball at ?

What is the velocity of the ball at ?

**Q20: **

While observing a spacecraft land on a distant asteroid, scientists noticed that the craft was falling at a rate of 5 m/s. When it was 100 m closer to the surface of the asteroid, the craft reported a velocity of 8 m/s. According to their data, what is the approximate gravitational acceleration on this asteroid?

**Q22: **

A small rocket with a booster blasts off vertically upward. When at a height of 5.00 km and velocity of 200.0 m/s, the rocket releases its booster stage. The rocket continues to accelerate upward, while the booster stage is accelerated only by gravity.

What is the maximum height that the booster stage reaches?

What is the speed of the booster stage when it is at a height of 6.00 km?

**Q23: **

The height of a ball falling from the roof of a building that is 98 meters high to the street below, at 1.0-second intervals, is shown in the diagram. The ball has a vertically downward speed of 4.9 m/s at the instant time .

What is the value of when the ball reaches the ground?

What is the speed of the ball when it reaches the ground?