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## Homework Statement

A baseball is given an initial velocity with magnitude [tex]v_{0}[/tex] at an angle of [tex]\phi[/tex] above the surface of an incline, which is in turn inclined at an angle [tex]\theta[/tex] above the horizontal.

a) Calculate the distance measured along the incline from the launch point to where the baseball strikes the incline. In terms of [tex]v_{0}, g, \theta, \phi[/tex].

b) What angle [tex]\phi[/tex] gives the maximum range, measured along the incline.

## Homework Equations

[tex]x_b = v_{0}\cos{(\theta+\phi)}t[/tex]

[tex]y_b = v_{0}\sin{(\theta+\phi)}t - \frac{1}{2}gt^2[/tex]

[tex]y_i = x\tan{\theta}[/tex]

## The Attempt at a Solution

Part a) is fairly straightforward to solve... eliminating t to find [tex]y(x)[/tex] and letting [tex]y_i = y_b[/tex] yields:

[tex]d = \frac{2v_{0}^2}{g}\frac{\cos^2{(\theta+\phi)}}{\cos{\theta}}\left[\tan{(\theta+\phi)}-\tan{\theta}\right][/tex]

Which is the solution to a). Just having trouble finding a worked solution for part b). My maths is a little shaky, can someone walk me through it? It's easy enough to find a partial derivative for d, but I still can't solve it for 0.