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One side of the roof of a building slopes up at 33.5°. A roofer kicks a round, flat rock that has been thrown onto the roof by a neighborhood child. The rock slides straight up the incline with an initial speed of 15.0 m/s. The coefficient of kinetic friction between the rock and the roof is 0.430. The rock slides 10.0 m up the roof to its peak. It crosses the ridge and goes into free fall, following a parabolic trajectory above the far side of the roof, with negligible air resistance. Determine the maximum height the rock reaches above the point where it was kicked.

Use conservation of energy to determine the velocity of the rock when it reaches the peak:

$<br /> \frac 1 2 m v_1 ^2 - Fd -mgd \sin \theta= \frac 1 2 m v_2^2<br />$

where F is the force of friction $F=\mu mg \sin \theta$ and d is the length of roof that the rock slides over. This gives you v2, and you can use

$<br /> (v_2 sin \theta)^2 = 2 g h$

to determine the height h above the peak of the roof that the rock reaches.

Thank you sooo much!