A football is kicked as shown in Figure. The angles θ and ϕ locate the point of maximum height, then find the relation between α, θ and ϕ.

Question

G1 Physics · Accepted Answer

For a projectile landing at the launch level, the highest point is midway in horizontal range. Therefore the two lines joining the highest point to the launch and landing points make equal angles: θ = ϕ. Also H/R = tanα/4, so tanθ = H/(R/2) = 2H/R = tanα/2. Hence tanα = 2tanθ = tanθ + tanϕ. Therefore option D.