The idea
For a launch speed u at angle θ above the horizontal, the initial components are u cos θ horizontally and u sin θ vertically. At the highest point, vertical velocity is zero, but horizontal velocity is generally not zero. These equations assume a uniform gravitational field and negligible air resistance.
Worked example
A ball leaves a horizontal ledge at 6 m/s and falls 4.9 m. Use g = 9.8 m/s². How far horizontally does it travel before landing?
- Vertical initial velocity is zero, so 4.9 = ½ × 9.8 × t².
- t² = 1 and the positive flight time is 1 s.
- Horizontal distance = 6 × 1 = 6 m.
A mistake to avoid
Do not use the horizontal launch speed as the initial vertical velocity. The two components belong in separate equations.
Check your understanding
What happens to the horizontal distance if the horizontal launch speed doubles from the same height?
Show the explanation
It doubles. The vertical fall and flight time are unchanged, so horizontal distance is proportional to horizontal speed.
Explore the lesson
This guide connects to Projectile Motion in the IB Physics course. The first two published lessons per subject are free previews; further interactive lessons require an account.