You are climbing in the High Sierra where you suddenly find yourself at the edge

Question

You are climbing in the High Sierra where 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 10.0 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 = (10-t)*330 ---->via sound h = (1/2)*g*t^2--->via rock 4.9t^2 = 3300-330t 4.9t^2 + 330t -3300 = 0 Using the quadratic formula: t = 8.8397 s ---> time for rock to hit ground Height of cliff: h = (1/2)*9.8*8.8397^2 = 382.9 m Height of cliff without sound correction: (1/2)*9.8*10^2 = 490 m In this case, you overestimated the height of the cliff: 490 m > 382.9 m Either way, you're in big trouble if you fall off.

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