Projectile Motion Problems with Solutions and Explanations

A collection of projectile motion problems with detailed solutions. These problems are best understood after reviewing the fundamental projectile equations. An interactive HTML5 simulation is available to visualize projectile motion concepts.

Problems with Detailed Solutions

Problem 1

An object is launched at a velocity of \(20 \text{ m/s}\) at an angle of \(25^\circ\) above the horizontal.
a) What is the maximum height reached?
b) What is the total flight time?
c) What is the horizontal range?
d) What is the magnitude of velocity just before impact?

Solution to Problem 1

Problem 2

A projectile is launched from point \(O\) at \(22^\circ\) with initial velocity \(15 \text{ m/s}\) up an incline plane at \(10^\circ\) to the horizontal. It impacts the plane at point \(M\).
a) Find the time of impact.
b) Find the distance \(OM\).

Projectile on an inclined plane

Solution to Problem 2

Problem 3

A projectile is launched at \(30^\circ\) to clear a pond of length \(20 \text{ m}\).
a) What initial velocity range ensures it lands between points \(M\) and \(N\)?

Projectile clearing a pond

Solution to Problem 3

Problem 4

A ball is kicked at \(35^\circ\) to the ground.
a) What initial velocity is required to hit a target \(30 \text{ m}\) away and \(1.8 \text{ m}\) high?
b) What is the time to reach the target?

Projectile ball hitting a target

Solution to Problem 4

Problem 5

A ball kicked from ground level at \(60 \text{ m/s}\) and angle \(\theta\) achieves a horizontal range of \(200 \text{ m}\).
a) Determine \(\theta\).
b) Find the time of flight.

Solution to Problem 5

Problem 6

A \(600\text{-g}\) ball is kicked at \(35^\circ\) with initial velocity \(V_0\).
a) Find \(V_0\) given its kinetic energy at maximum height is \(22 \text{ J}\).
b) Determine the maximum height.

Solution to Problem 6

Problem 7

A projectile launched from ground hits a target \(1000 \text{ m}\) away after \(40 \text{ s}\).
a) Find the launch angle \(\theta\).
b) Determine the initial velocity.

Solution to Problem 7

Problem 8

The trajectory of a projectile is given by \(y = -0.025 x^{2} + 0.5 x\) (coordinates in meters).
a) Find the initial velocity and launch angle.

Solution to Problem 8

Problem 9

Two balls (A: \(100 \text{ g}\), B: \(300 \text{ g}\)) are pushed horizontally from a \(3\text{-m}\) table. Initial velocities: \(v_A = 10 \text{ m/s}\), \(v_B = 15 \text{ m/s}\).
a) Find the time each hits the ground.
b) Find the horizontal distance between impact points.

Solution to Problem 9