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 $\theta = 30^o$ wrt to the horizon, throws a stone at ${\bf v} = 16$ m/s up the hill at an angle $\phi = 65^o$ wrt to the horizon. Find $y_f$.

2. Relevant equations

$$y_f = v_{y_i}t + \frac{1}{2}a_yt^2$$

$$v_{x_i} = \frac{x_f}{t}$$

3. The attempt at a solution

My thought process is the first find time (t), then solve for $y_f$.

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

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

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