Serway & Jewett — Motion in Two Dimensions: Problem 50

A projectile is fired up an incline (incline angle \(\phi\)) with an initial speed \(v_i\) at an angle \(\theta_i\) with respect to the horizontal (\(\theta_i > \phi\)) as shown in Figure P4.50. (a) Show that the projectile travels a distance \(d\) up the incline, where \[ d = \frac{2v_i^2 \cos \theta_i \sin(\theta_i - \phi)}{g \cos^2 \phi} \] (b) For what value of \(\theta_i\) is \(d\) a maximum, and what is that maximum value?