A large building has an inclined roof. The length of the roof is 48.5 m and the

Question

A large building has an inclined roof. The length of the roof is 48.5 m and the angle of the roof is 17.0° below horizontal. A worker on the roof lets go of a hammer from the peak of the roof. Starting from rest, it slides down the entire length of the roof with a constant acceleration of 2.87 m/s2. After leaving the edge of the roof, it falls a vertical distance of 23.0 m before hitting the ground. (a) How much time does it take the hammer to fall from the edge of the roof to the ground? s (b) How far horizontally does the hammer travel from the edge of the roof until it hits the ground?

Explanation / Answer

At the edge of the roof, v² = u² + 2as = 0 + 2 * 2.87m/s² * 48.5m = 278.39 m²/s²
v = 16.68 m/s
Then Vx = 16.68m/s * cos-17º = 15.95 m/s
and Vy = 16.68m/s * sin-17º = -4.87 m/s

(a) s = So + Vo*t + ½at²
0 = 23m - 4.87m/s*t - 4.9m/s²*t²
roots at t =1.725 s take positive root

(b) x = Vx * t = 15.95m/s * 1.725s = 27.51 m

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