# Lesson Worksheet: Horizontal Projectile Motion Mathematics

In this worksheet, we will practice solving problems about projecting bodies horizontally from a point above the ground.

**Q1: **

A particle was projected horizontally from a point 42 m above the ground at 32 m/s. Find, to one decimal place, the time it took the particle to reach the ground. Take .

**Q2: **

A ball is rolled along a smooth horizontal surface from a point 6 m away from the edge of the surface with an initial velocity of 30 m/s. Given that the surface is suspended 2.5 m above the ground, find the total time taken for the ball to reach the ground from its initial position. Give your answer to 2 significant figures. Take the acceleration of gravity .

**Q3: **

An arrow is fired horizontally from a bow at a target at a speed of 74 m/s. The arrow hits the target at a point 15 cm below the point from which it left the bow. Modeling the arrow as a projectile moving freely under gravity in a vertical plane perpendicular to the plane of the target, find the horizontal distance between the bow and the target. Give your answer to two decimal places.

**Q4: **

Liam threw a ball horizontally at a speed of 10.5 m/s toward a vertical target. The ball moved freely under gravity in a plane perpendicular to the target and hit the target at a height 12.1 cm below the height from which it was thrown. Taking , find the horizontal distance the ball traveled.

**Q5: **

A rock was thrown horizontally from the top of a tower at 20.8 m/s. It flew for 2.4 seconds before hitting the ground. Calculate the distance between the base of the tower and the point where the rock landed, and find the height of the tower. Take

- A,
- B,
- C,
- D,
- E,

**Q6: **

Jackson threw a stone horizontally at 30 m/s from the top of a cliff. Given that it landed on the ground 32 meters below, find the distance between Jackson and where the stone landed to the meter. Take .

**Q7: **

A ball is thrown horizontally from the top of a tower of height 150 m. It lands on the ground at a horizontal distance of 100 m from the base of the tower. Find the initial velocity at which the ball is thrown, taking the acceleration due to gravity . Give your answer to two decimal places.

**Q8: **

A particle is projected horizontally at an initial velocity of m/s from a point 30 m above the ground. The particle lands at a horizontal distance of 200 m from the point of projection. Assuming that the particle moves freely under gravity, find . Give your answer to 3 significant figures. Take the acceleration of gravity .

**Q9: **

A brick of mass 3 kg is projected along a rough plane at 10 m/s. After traveling for 8 m, the brick leaves the plane and falls 2.5 m to the ground. The total time of motion from the moment of projection to landing on the ground is 2 s, and the acceleration of gravity is .

Find, to one decimal place, the total time that the brick is in contact with the rough plane.

Find, to one decimal place, the coefficient of friction between the brick and the plane.

Find, to one decimal place, the horizontal distance from the point of projection to the point where the brick lands.

**Q10: **

Mason was honing his stone-skimming skills at a lake. He finds that for the stone to skim well it must hit the surface of the lake at an angle of or less to the horizontal. What is the minimum speed at which he must throw the stone for it to skim well, given that he throws it horizontally from a height of 96 cm? Give your answer in meters per second, correct to one decimal place. When he throws the stone at this speed, at what distance does the stone first hit the water? Give your answer in meters, correct to one decimal place. Take .

- A,
- B,
- C,
- D,
- E,