CLASS 11–12 PHYSICS · MOTION IN A PLANE

Projectile motion: time, height and range

For a projectile launched at speed u and angle θ (no air resistance): T = 2u sinθ/g, H = u² sin²θ/(2g), R = u² sin2θ/g. Horizontal launch from height h: t = √(2h/g), range = u·t.

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Worked examples

Example 1 · level 1

A ball rolls off the edge of a flat roof 45 m high in Surat with a horizontal speed of 20 m/s. How far from the foot of the building does it land (in m)? Take g = 10 m/s².

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t = √(2h/g) = √(9) = 3 s.
x = 20 × 3 = 60 m.

Answer: 60 m

Example 2 · level 2

A football is kicked at 40 m/s at 30° above the horizontal. Find the time of flight (in s). Take g = 10 m/s².

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T = 2 × 20 ÷ 10 = 4 s.

Answer: 4 s

Example 3 · level 3

A javelin is thrown at 40 m/s at 60° to the horizontal. Find its horizontal range (in m, correct to 2 decimal places), ignoring air resistance and the thrower's height. Take g = 10 m/s².

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R = 40² × sin 120° ÷ 10
= 1600 × 0.866 ÷ 10 = 138.56 m.
Note: 60° and 30° give the same range.

Answer: 138.56 m