A projectile has range equal to 3/4 of the maximum range possible with the same speed. If t=tanθ, which values of t are possible?

Question

G1 Physics · Accepted Answer

For fixed speed, R/Rₘₐₓ = sin2θ = 3/4. Using sin2θ = 2tanθ/(1+tan²θ), we get 2t/(1+t²)=3/4. Thus 8t = 3+3t² ⇒ 3t²−8t+3=0. Therefore t = [8±√(64−36)]/6 = (4±√7)/3. Hence A and B are correct.