Projectile components

Objective. Resolve initial velocity and form component equations.

1. Learn
2. Worked example
3. Practice
4. Feedback
5. Continue

Learn: the key idea

Projectile components describes resolving an initial velocity at launch angle θ into independent horizontal and vertical parts: horizontal component ux = u cos θ, remaining constant since there is no horizontal force, and vertical component uy = u sin θ, which changes under constant gravitational acceleration g acting downward. Each component is then tracked separately using the constant-acceleration (suvat) equations, with horizontal displacement x = ux t and vertical displacement y = uy t − ½gt². For example, a ball launched at 20 m/s at 30° has ux = 20cos30° ≈ 17.3 m/s and uy = 20sin30° = 10 m/s.

Worked example

A projectile is launched at 28 m/s at 60° to the horizontal. Find the horizontal and vertical components of the initial velocity.

1 $Horizontal component: ux = u cos θ = 28 cos 60°$
2 $ux = 28 \times 0.5 = 14 m/s$
3 $Vertical component: uy = u sin θ = 28 sin 60°$
4 $uy = 28 \times (\sqrt3/2) \approx 24.2 m/s$

Answer: ux = 14 m/s, uy ≈ 24.2 m/s

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. Students apply gravity to the horizontal component or keep the vertical component constant. Remember gravity only affects the vertical component; the horizontal component stays constant throughout the flight.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard