During a winter storm a roof shingle breaks free from the very top of a house...

During a winter storm a roof shingle breaks free from the very top of a house . The shingle slides starting from rest down the 6.0m long icy roof that is inclined at 30°. The edge of the roof is 4.0m above ground level. How far from the base of the house does the roof shingle land?

Expert Solution

Assuming the roof has no friction, the acceleration will be

a = gsinθ
a = g/2

The velocity at the eave is found using

v² = u² + 2as
v² = 2(g/2)s
v² = 2(9.8/2)6.0
v² = 58.8
v = 7.668 m/s

now find the time needed to traverse the distance from eave to ground

s = s0 + ut + ½at²

Assuming the origin at the eave and down being the positive direction

4.0 = 0 + (7.668sin30)t + ½9.8t²
0 = 4.9t² + 3.8t - 4.0

quadratic formula

t = (-3.8 ±√(3.8² - 4(4.9)(-4.0))) / (2(4.9))

t = 0.595 s

the horizontal distance the shingle travels from the eave to the ground is

s = vt
s = (7.668cos30)(0.595)
s = 3.951
Or
s = 4.0 m

genius_generous answered 2 years ago

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