Projectile Motion Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Projectile Motion.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

Two-dimensional motion under gravity alone, where horizontal velocity is constant and vertical motion is uniformly accelerated — producing a parabolic path.

A thrown ball follows a curved path—horizontal motion is steady, vertical is accelerated.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Horizontal and vertical motions are independent—analyze separately, then combine.

Common stuck point: The horizontal velocity stays constant (no horizontal acceleration).

Sense of Study hint: When solving a projectile problem, split the motion into horizontal (x) and vertical (y) components. Horizontally, velocity is constant: x = v_{0x} t. Vertically, use free-fall equations with a = -g. Find the time of flight from the vertical equation, then use it to find the horizontal range.

Worked Examples

Example 1

medium
A ball is launched horizontally at 15 \text{ m/s} from a cliff 45 \text{ m} high. How far from the base of the cliff does it land? Use g = 10 \text{ m/s}^2.

Solution

  1. 1
    Use vertical motion to find the time to fall: t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 45}{10}} = \sqrt{9} = 3 \text{ s}
  2. 2
    Horizontal speed stays constant because there is no horizontal acceleration.
  3. 3
    Horizontal distance: x = v_x \cdot t = 15 \times 3 = 45 \text{ m}

Answer

x = 45 \text{ m}
In projectile motion, horizontal and vertical motions are independent. The horizontal velocity remains constant (no air resistance), while the vertical motion is free fall.

Example 2

hard
A projectile is launched at 40 \text{ m/s} at 30° above the horizontal. What is the maximum height and horizontal range? Use g = 10 \text{ m/s}^2.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A ball is kicked at 20 \text{ m/s} at 45°. What is the range? Use g = 10 \text{ m/s}^2.

Example 2

hard
A ball is kicked horizontally off a 45 \text{ m} high cliff at 20 \text{ m/s}. Using g = 10 \text{ m/s}^2: (a) How long until it hits the ground? (b) How far from the base of the cliff does it land?
← Back to Projectile Motion Formula Explained Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

free fallvelocityvectors