# Exercises on Projectile Motion

*Helena Dedic*

## Contents

## Exercise 1

An object is launched from the ground at some angle above horizontal. Three seconds later, its velocity v is (20 m/s, -4 m/s). Find how far (horizontally) and how high the object will fly.

## Exercise 2

A balloon is drifting horizontally with a speed of 15 m/s. A bolt drops from the balloon at a height of 100 m above the ground. Use the v - t graphs to solve this problem.

When will the bolt land on the ground?

How far from the drop point will it land? Compute the horizontal distance.

What is the bolt's velocity 2 s into the flight?

With what velocity will it land?

## Exercise 3

Amorosa, who is on a balcony 40 m above the ground, throws the key to her heart at 37° below the horizontal to Pedro on the ground. He catches the key two seconds after it was thrown.

How far from the base of the building was he standing?

At what angle was the key moving when he caught it?

## Exercise 4

A rocket launched from rest at to the horizontal has a constant net acceleration of 8 m/s2 along this direction for 6.5 s and then is in free fall. Find its maximum height and its range.

## Exercise 5

A tennis ball is served at a height of 2.4 m at 30 m/s in the horizontal direction. The net is 0.9 m high at a horizontal distance of 12 m. Does the ball clear the net? If so, by how much? If not, where does it strike the net?

## Exercise 6

The path of a projectile is given below. Sketch the position, velocity and acceleration vectors for the projectile in the position shown and write the components of acceleration.

## Exercise 7

Jack, standing on a cliff, throws a rock into a lake 20 m below with initial velocity 25 m/s at 53° above horizontal.

How high above the water will the rock rise?

How far from the cliff (along horizontal) will the rock land?

With what velocity will it land?

## Exercise 8

A plane flying horizontally dropped a supply of blankets for stranded hunters. The blankets landed 4 s after the drop with a speed of 50 m/s.

What were the components of the velocity when the supply landed?

What was the velocity of the plane?

How high was the plane flying?

How far did the blankets move in the horizontal direction?

## Exercise 9

A balloon is launched from rest from the ground. By the time it rises to a height of 40 m its velocity is 20 m/s in the direction of 37° above horizontal. Let us choose to call this time t = 0 and this horizontal position x = 0. Assume the balloon maintains this velocity and that, as it reaches 100 m above ground, a bolt drops from the balloon. Use v - t graphs to solve the following:

When will the bolt hit the ground counting from what we called t = 0?

How far away will it land? Compute horizontal distance counting relative to x = 0.

With what velocity will it land?

## Exercise 10

A ball rolls of a 1 m-high table and lands 1.6 m along the floor. Find its initial speed and the time of flight.

## Exercise 11

A projectile fired from the ground has a velocity of at a height of . Find the initial velocity and the maximum height.

## Exercise 12

A ball is thrown from ground level. Three seconds later it is moving horizontally at 15 m/s. Find the horizontal range and the angle of impact.