A golf ball is hit with an initial speed 0 at an angle a to the horizontal from a point that lies at the

A golf ball is hit with an initial speed ν₀ at an angle a to the horizontal from a point that lies at the foot of a straight-sided hill that is inclined at an angle ϕ to the horizontal, where

Show that the ball lands at a distance

measured up the face of the hill. Hence, show that the greatest range that can be achieved for a given ν₀ occurs when α = (ϕ/2) + (π/4), i.e., when the initial velocity vector bisects the angle between the vertical and the hill.

0 < p