# Worksheet: Projectile Motion

In this worksheet, we will practice analyzing the motion of objects that move horizontally while undergoing constant vertical acceleration.

**Q1: **

A projectile is fired with an initial speed of 28 m/s and has a maximum upward vertical displacement from its launch position of 4.4 m. What angle above the horizontal is the projectile launched at?

**Q2: **

A projectile has an initial speed of 25 m/s and is fired at an angle of above the horizontal. What is the time between the projectile leaving the ground and returning to the ground at the same height that it was launched from?

**Q3: **

The change in the vertical displacement of a projectile from its launch position and its horizontal displacement from its launch position is shown in the graph. Which of the following graphs most correctly represents how the mechanical energy of the projectile changes from the instant that it is launched to the instant that it lands?

- A
- B
- C
- D
- E

**Q4: **

A frog jumps from the ground and lands at a point 16 cm horizontally distant from its launch point, moving with constant horizontal velocity. The maximum vertical displacement of the frog above the ground during its leap is 3.6 cm. What is the horizontal velocity of the frog?

**Q5: **

A projectile is fired at an angle of above the horizontal and has a maximum upward vertical displacement from its launch position of 7.2 m. What is the initial speed of the projectile?

**Q6: **

A projectile is fired at an angle of above the horizontal with an initial speed of 44 m/s. What is the maximum upward vertical displacement of the projectile from its launch position?

**Q7: **

A projectile has an initial speed of 15 m/s at a launch angle of above the horizontal. What is the horizontal displacement of the projectile from its launch position to where it lands if its vertical displacement from its launch position is zero?

**Q8: **

Two projectiles are launched along the same horizontal direction from the same point at the same time. Projectile is launched at an angle of above the horizontal at a speed of 2.5 m/s. Projectile is launched at an angle of above the horizontal. The projectiles land at the same point. At what speed was projectile launched?

**Q9: **

A projectile is fired at an angle of above the horizontal. The time between the projectile leaving the ground and returning to the ground at the same height that it was launched from is 2.9 s. What was the projectile’s initial speed?

**Q10: **

A ball is launched diagonally upward and then returns to the ground. The change of the vertical displacement of the ball with time is shown in the graph. The ball lands a 2.4 m horizontal distance from where it was launched. The ball has a constant horizontal speed throughout its flight.

What is the initial vertically upward speed of the ball?

What is the horizontal speed of the ball?

At what angle above the horizontal is the ball launched?

**Q11: **

A ball is thrown horizontally from an athlete’s hand with a constant horizontal velocity and bounces when it hits the ground. The ball rebounds from the ground at an angle of above the horizontal at a speed of 2.2 m/s.

How far does the ball travel horizontally between the first and the second time it hits the ground?

What is the maximum vertically upward displacement of the ball after it bounces?

**Q12: **

A ball is launched vertically upward and then returns to the ground. The change of the vertical displacement of the ball with time is shown on the graph. The maximum vertically upward displacement of the ball from its launch point is 5.0 m.

What is the initial vertical velocity of the ball?

What is the speed of the ball at point where its upward vertical displacement from its launch point is 4.5 m?