# Throwing a rock up a hill

**1. The problem statement, all variables and given/known data**

I was tutoring the other day, when we came across a problem that had me stumped!

A person standing on a hill that forms an angle [itex] \theta = 30^o [/itex] wrt to the horizon, throws a stone at [itex] {\bf v} = 16 [/itex] m/s up the hill at an angle [itex] \phi = 65^o [/itex] wrt to the horizon. Find [itex] y_f [/itex].

**2. Relevant equations**

[tex] y_f = v_{y_i}t + \frac{1}{2}a_yt^2 [/tex]

[tex] v_{x_i} = \frac{x_f}{t} [/tex]

**3. The attempt at a solution**

My thought process is the first find time (t), then solve for [itex] y_f [/itex].

Initially I thought to take the ratio of [itex] v_x [/itex] and [itex] v_y [/itex], which would result in an equation involving [itex] tan(\phi – \theta) [/itex], but it involves too many unknowns (t, [itex] x_f [/itex]).

I know I need to utilize the angles in someway, and that finding [itex] h_{max}, R [/itex] will not help in this situation. Any suggestions on how to start this problem would be greatly appreciated!

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