Chapter 4, Problem 50CP

A projectile is fired up an incline (incline angle ϕ) with an initial speed v_i at an angle θ_i with respect to the horizontal (θ_i > ϕ) as shown in Figure P4.50. (a) Show that the projectile travels a distance d up the incline, where

$d=\frac{2v_i^2\cos {\theta }_i\sin ({\theta }_i-\varphi )}{g{\cos }^2\varphi }$

(b) For what value of 0_i is d a maximum, and what is that maximum value?

Figure P4.50