Intro to Projectile Motion: Horizontal Launch Practice Problems

A playground is located 3.5 m from the base of a cliff. This 3.5 m wide zone from the cliff's base is used by cheering spectators. A player at the top of the cliff launches a 4.50 N ball horizontally. What must be the minimum speed of the ball as it leaves the top of the cliff so that it misses the spectator area at the base of the cliff? The spectator area is 3.5 m wide and 12.0 m below the top of the cliff. 

You are having fun in a storey building. You drop a stone downward from the window and notice it reaches the ground in 3.2 s. You now launch a ball horizontally with an initial speed of 1.9 m/s. Ignoring air resistance, at what length, measured from the base of the storey does the ball hit the ground?

You place a metallic sphere on a horizontal board. You accidentally hit the sphere, where it rolls off the board with a speed of 2.5 m/s. It hits the floor in 0.582 s. Calculate the height of the board measured above the floor. Ignore air resistance.

A rocket is launched at an angle of θ and a take-off speed of 90 m/s. The total distance in the x-direction covered by the rocket is represented by the equation (8100•sin 4θ)/g. Determine the angle θ for which the rocket will cover 3/4 of the maximum range.

A missile is fired with a take-off speed of 120 m/s at an angle θ with respect to the ground. It experiences a horizontal acceleration of 50 m/s² along the x-axis in a direction opposite to the motion. Determine the value of θ so that the missile will cover the maximum distance.

Hint: use the following expression d/dθ(A•cosθ•sinθ - B•sin²θ) = A•cos(2θ) - B•sin(2θ)

A golf ball is hit with a speed of 40 m/s making an angle θ above the horizontal. The ball faces an acceleration along the x-axis opposing its motion which is 15 % of the acceleration due to gravity. Calculate the value of θ so that the ball reaches a maximum horizontal distance.

Hint: use the following expression d/dθ(A•cosθ•sinθ - B•sin²θ) = A•cos(2θ) - B•sin(2θ)

A football is kicked from a cliff with a takeoff speed of 30 m/s and a launch angle of 35°. Calculate the angle of the ball after it has covered a horizontal distance of 75 m.

Consider an imaginary concept that the Olympics are held on another planet whose gravitational acceleration is 1/10 times its value on earth. During the event of javelin throw, the spear is launched at an angle of 45 degrees with respect to horizontal and a takeoff speed of 20 m/s. Determine the difference between a spear's time of flight on the imaginary planet and its time of flight on earth.

A rocket is fired parallel to the ground from a cliff. The rocket meets the ground 75 m away at an angle of 5.0° with the horizontal. Determine the takeoff speed of the rocket. Ignore air resistance.

During a film shoot, a stuntman has to jump off a moving car, which takes off from the cliff and crashes on the ground 30m away after 1.5 s. Determine the speed of the car as it takes off from the cliff. Assume there is no air resistance.

A gardener is watering his plants on sloppy land inclined at 20° as shown in the figure below. The water is leaving the pipe at an angle of θ° with respect to the slope. Determine the angle at which the water should leave the pipe so that it covers the maximum distance 'd'.

Hint: use the following expression d/dθ(A•cosθ•sinθ - B•sin²θ) = A•cos(2θ) - B•sin(2θ)

A motorcyclist is contemplating a leap from a cliff as shown in the figure below. The cliff stands 5.0 m above the water's surface, and the pool extends horizontally for 18 m. If the motorcyclist aims to clear the pool completely, what is the minimum horizontal velocity required for a successful jump?

An engineer is testing a new lightweight drone by launching it horizontally from a platform to see how far it can travel without propulsion. There's a fence 5.50 meters tall located 30.0 meters from the launch platform. The drone is launched from a height of 8.40 meters above the ground. What is the minimum horizontal speed required for the drone to clear the fence? Will it land safely in the designated area that starts 10.0 meters beyond the fence and extends for another 20.0 meters? Determine the total time the drone will be in the air from the moment of launch to when it lands.

A basketball is passed between two players standing 10 meters apart on the same horizontal plane. If the ball is thrown with an initial velocity of 15 m/s horizontally, estimate by what percentage gravity changes the magnitude of the ball's velocity when it is caught by the receiving player. Assume no air resistance and spin effects.

A pitcher releases a baseball horizontally at a velocity of 15 m/s from a height of 1.5 m. The batter is positioned 20 m away. Neglecting air resistance, determine the vertical distance the ball will drop by the time it reaches the batter.