1. A physics student drops a rock from a high cliff to the river below. The time

Question

1. A physics student drops a rock from a high cliff to the river below. The time from the beginning of the drop until she hears the sound of the rock hitting the water below is 10.0 seconds. The velocity of sound in air is 340 m/s.

(a) How high above the water is the cliff?

(b) From what height would she have to drop an object so that the time it takes to fall is equal to the time it takes the sound to return?

Tree Hill 0 (p 2. A vertical tree of height h casts a shadow of length s on a hillside that slopes upward with angle o relative to the horizontal. The sun's elevation makes an angle with respect to the horizon. Derive an expression giving h in terms of S, and .

Explanation / Answer

1a] Let the height of cliff be h, then

time taken by sound to return + time taken by rock to drop = total time

h/vsound + sqrt (2h/g) = total time

h/340 + sqrt (2h/9.8) = 10

solving this ,

h = 385 m answer

b] time taken by sound to return = time taken by rock to drop

   h/340 = sqrt (2h/9.8)

h = 23592 m answer

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