One side of the roof of a house slopes up at 37.0°. A roofer kicks a round, flat

Question

One side of the roof of a house slopes up at 37.0°. 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 0.400. 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

Using Fnet = ma, perpendicular to the incline,

N - mg cos37 = 0

N =mgcos37

and friction force, f = ukN = 0.4 mg cos37

now along the incline,

Fnet = - mgsin37 - f = ma

- mgsin37 - 0.4mgcos37 = ma

a = - 9.8(sin37 + 0.4cos37) = - 9.03 m/s^2

using vf^2 - vi^2 =2ad

vf^2 - 15^2 = 2(-9.03)(10)

vf = 6.67 m/s

so rock will free fall with 6.67 m/s at angle of 37 deg .

in vertical,

uy = 6.67sin37 = 4.01 m/s

it will go upto until its vertical component of velocity becomes zero.

using vf^2 - vi^2 = 2 ad in vertical,

0^2 - 4.01^2 = 2(-9.8)h

h =0.821 m

height of peak of roof from launching point, h' = dsin37 = 10sin37 = 6.02 m

Hmax =h + h' = 6.84 m

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