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

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