One side of the roof of a building slopes up at 44.5°. A roofer kicks a round, f

Question

One side of the roof of a building slopes up at 44.5°. 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 0.335. 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.

Explanation / Answer

Here ,

acceleration at incline , a = g *(cos(theta) * uk + sin(theta))

a = 9.8 *(cos(44.5) * 0.335 + sin(44.5))

a = 9.21 m/s^2

let the speed at the top of incline is v

v^2 - 15^2 = 2 * 9.21 * 10

v = 6.4 m/s

Now, maximum height = 10 * sin(44.5) + (6.4 * sin(44.5))^2/( 2* 9.8)

maximum height = 8.03 m

the maximum height the rock reaches above the point where it was kicked is 8.03 m

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