Projectiles

A projectile is anything thrown or launched that then moves only under gravity. Split the motion into horizontal (constant speed) and vertical (constant acceleration g downwards), linked by time.

Key facts

  • Horizontal: x = (u cos θ)t.
  • Vertical: y = (u sin θ)t − ½gt².
  • Time of flight on level ground: 2u sin θ / g.
  • Range: u² sin 2θ / g, greatest at 45°.
  • At the highest point the vertical velocity is zero.

Worked examples

Example 1

A ball is kicked at 20 m/s at 30° above the horizontal. Find the time of flight and range (g = 9.8).

  1. Vertical: u sin 30° = 10 m/s. Horizontal: 20 cos 30° = 17.3 m/s.
  2. Time: 2 × 10 / 9.8 = 2.04 s.
  3. Range: 17.3 × 2.04 = 35.3 m.

Answer: 2.04 s, 35.3 m