Question

Two golf balls are hit from a flat field, each at an angle 30o above the horizontal. Initial speed of ball 2 is twice the initial speed of ball 1. If ball 1 and ball 2 land a distance d1 and d2 respectively. What is the ratio of d2/d1

Answer 1

The range, R, of a projectile based on its angle of projection ∅ and velocity v can be directly calculated by:
R = (v²sin2∅)/g
Let the v of ball 1 be v₁
R₁ = (v₁²sin(2*30))/g
v₂ = 2v₁
R₂ = ((2v₁)²sin(2*30))/g
R₂ = 4[(v₁²sin(2*30))/g]
R₂ = 4R₁
So ratio of d2/d1 = 4