Projectile motion (no air resistance): angle for maximum horizontal range A projectile is launched with a given speed. At what angle of projection is the range greatest?

Given data

• Projectile launched with speed u; no air resistance; flat ground.

Concept/Approach

• Range R = (u²/g)·sin 2θ. R is maximized when sin 2θ = 1.

Step-by-stepsin 2θ = 1 → 2θ = 90° → θ = 45°.

Final Answer45°