Question #167460

Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground.

Expert's answer

**Q167460**

Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground.

**Solution: **

We are not provided the air resistance in this problem, so we will consider the free fall of the roof

shingles under earth's gravitational force.

We will use the formula which relates the acceleration a, displacement s, and time t.

The formula of the second equation of motion will be useful here.

"s = ut + \\frac{1}{2}* a * t^2"

's' is the displacement. 'a' is the acceleration. 't' is the time in seconds.

'u' is the initial velocity.

Since the given object is falling under gravitational force, so we will have to take into consideration the

gravitational acceleration.

s = 8.52m, a = 9.8 m/s^{2} , u = initial velocity = 0 m/s

substitute all the information in the formula we have

"8.52m = 0m\/s * t + \\frac{1}{2}* 9.8m\/s^2 * t^2"

"8.52 m =0 + \\frac{1}{2}* 9.8m\/s^2 * t^2"

"8.52 m = \\frac{1}{2}* 9.8m\/s^2 * t^2"

Arranging this equation for t, we have

"t^2 = \\frac{8.52m * 2 }{9.8m\/s^2}"

"t^2 = 1.739 s^2"

taking square root on both the side we have

"t = \\sqrt{1.739 s^2 } = 1.3186 s"

In the question, we are given the distance, 1.82m in 3 significant figures. Hence

our final answer must also be in 3 significant figures.

t = 1.32 seconds .

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