Serway & Jewett — Motion in Two Dimensions: Problem 52

In the What If? section of Example 4.5, it was claimed that the maximum range of a ski jumper occurs for a launch angle \(\theta\) given by \[\theta = 45^{\circ} - \frac{\phi}{2}\] where \(\phi\) is the angle the hill makes with the horizontal in Figure 4.15. Prove this claim by deriving the equation above.