One side of the roof of a building slopes up at 42.5°. A roofer kicks a round, f

Question

One side of the roof of a building slopes up at 42.5°. 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 0.390. 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.

_________________m

Explanation / Answer

Here,

let the maximum height of rock is h

Now, using conservation of energy

0.5 * m * 15^2 = m * 9.8 * 0.390 * h/sin(42.5 degree) + m * 9.8 * h

0.5 * 15^2 = 9.8 * 0.390 * h/sin(42.5 degree) + 9.8 * h

solving for h

h = 7.28 m

the maximum height reached is 7.28 m

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