A ball falls down from the roof of a high building. A student observes that time taken by the ball to travel last one fourth distance to be 0.45s. Determine the height of building?
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Answer:
S1 = 1/2 g t1^2 S1 = 3 H /4
S2 = 1/2 g t2^2 S2 = H
S2 / S1 = 1.33
S2 / S1 = 1/2 g t2^2 / (1/2 g t1^2) = 1.33 = (t2 / t1)^2
t2 = 1.155 t1
t2 - t1 = .45 = (1.155 - 1) t1
t1 = .45 / .155 = 2.91 s
t2 = 2.91 + .45 = 3.36 s
H = 1/2 g t2^2 = .5 * 9.8 * 3.36^2 = 55.3 m
Check: 3 H / 4 = .5 * 9.8 * 2.91^2 = 41.5
(55.3 - 41.5) / 55.3 = .25
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