Suppose you are climbing in the High Sierra when you suddenly find yourself at t

Question

Suppose you are climbing in the High Sierra when you suddenly find yourself at the edge of a fog-shrouded cliff. To find the height of this cliff, you drop a rock from the top and, 7.00 s later, hear the sound of it hitting the ground at the foot of the cliff.

Part A: Ignoring air resistance, how high is the cliff if the speed of sound is 330 m/s ?
Part B: Suppose you had ignored the time it takes the sound to reach you. In that case, would you have overestimated or underestimated the height of the cliff?

Explanation / Answer

h = (7-t)*330 ---->via sound
h = (1/2)*g*t^2--->via rock
4.9t^2 = 2310-330t
4.9t^2 + 330t - 2310 = 0

Using the quadratic formula:
t = 6.3931 s ---> time for rock to hit ground
Height of cliff:
h = (1/2)*9.8*6.3931^2 = 200.2 m

Height of cliff without sound correction:
(1/2)*9.8*7^2 = 960.4 m
In this case, you overestimated the height
of the cliff: 960.4 m > 200.2 m

Either way, you're in big trouble if you
fall off.

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