Q.Describe projectile motion in sport. Explain the factors that affect the flight of a projectile (angle of projection, speed of projection and height of release) and, using the range formula R = v^2 sin(2*theta)/g, explain why 45 degrees is the optimum angle of release on level ground.
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Start your 14-day free trial to unlock the full solution →A projectile moves freely under gravity; its flight depends on angle, speed and height of release, and the range formula shows 45° is optimal on level ground because sin(2θ) is then maximum.
Projectile motion in sport: A projectile is any body launched into the air that then travels freely under gravity alone — a javelin, shot, discus, or the body of a long-jumper. Its path is a symmetrical curve (parabola) when launched and landing at the same height.
R = (v² sin(2θ)) / g
where R = horizontal range, v = speed of projection, θ = angle of projection, g = acceleration due to gravity.
Factors affecting the flight:
- Angle of projection: the take-off angle. On level ground the range is maximum at 45°; steeper or shallower angles give a shorter range.
- Speed (velocity) of projection: range is proportional to v², so doubling the release speed quadruples the range — the single most powerful factor.
- Height of release: releasing from above the landing surface (e.g. shoulder height in a throw) extends the flight and lowers the optimum angle to a little under 45°.
- (Also gravity and air resistance/spin.)
Why 45° is optimum on level ground: For a fixed speed v, the range depends only on sin(2θ). …
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