A ground-to-ground projectile has horizontal range R and time of flight T. Which pair correctly gives the launch angle and launch speed?
Options

Question

A ground-to-ground projectile has horizontal range R and time of flight T. Which pair correctly gives the launch angle and launch speed?

G1 Physics · Accepted Answer

Horizontal motion gives u cosθ = R/T. Vertical motion over complete flight gives u sinθ = gT/2. Therefore tanθ = (u sinθ)/(u cosθ) = [gT/2]/[R/T] = gT²/(2R). Also u² = (u cosθ)²+(u sinθ)² = R²/T² + g²T²/4.