On hiking up a mountain that has several overhanging cliffs, a climber drops a s

Question

On hiking up a mountain that has several overhanging cliffs, a climber drops a stone at the first cliff to determine its height by measuring the time it takes to hear the stone hit the ground.

A) At a second cliff that is twice the height of the first, the measured time of the sound from the dropped stone is

less than double that of the first (WHY?)

B) If the measured time is 4.30s

for the stone dropping from the first cliff, and the air temperature is 20?C, how high is the cliff?

d=_____m  (answer is NOT 92.5)

C) If the height of a third cliff is three times that of the first one, what would be the measured time for a stone dropped from that cliff to reach the ground?

t=_____s ( answer is NOT 7.44)

Explanation / Answer

a) time to fall, y = 1/2 g t^2

t = sqrt( 2 y/g)

so doubling height causes time to go up by sqrt(2) for the fall

b)

t = t fall + tsound

4.3 = sqrt(2*h/9.81) + h/343

h=81 m

c) t = sqrt(2*3*81/9.81) + 3*81/343=7.75 s

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