Question

1)

To calculate the depth of a water well, an explorer drops a stone and with its stopwatch measures the time needed to hear the moment when the stone hits the water. Considering that the speed of sound in the air is 343m / s and the time elapsed to hear the sound is 4 seconds, what is the depth of the well?

2)

From a window that is 10m from the ground, a stone is dropped at the same moment a drop of water drops through the window with a speed of 10m / s. How long will it take between the two impacts with the ground? (Assume that the instant the stone is released, the drop of water is exactly at the same height).

Answer 1

ONE QUESTION AT A TIME PLEASE

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1) Let d be the depth

If time to reach bottom of well is t

then time taken by sound to come back

4 - t

assuming the stone is dropped from rest

d = 4.9t² ---------- (1)

d = 343 ( 4 - t)

d = 1372 - 343t ------- (2)

set (1) and (2) equal

we get a quadratic equation

4.9t² + 343t - 1372 = 0

t = - 343 +/- 380.18 / 9.8

t = 3.794 sec (ignore the negative value)

so,

d = 4.9 * 3.794²

d = 70.5 m