Ignoring air resistance, if the speed of sound is 343 m/s, how deep ℎ is the well?

Question

Imagine that you are standing at a wishing well, wishing that you knew how deep the surface of the water was. Cleverly, you make your wish. Then you take a penny from your pocket and drop it into the well. Exactly 3.50 s after you dropped the penny, you hear the sound it made when it struck the water.

Answer 1

Suppose h is the height.

Then time taken to hear sound = time taken for penny to hit the water + time taken for sound of penny hitting the water to reach you.

s = ut + 0.5at^2

s = h

u = 0

a = 9.8 m/s/s

so h = 4.9 t^2

t = sqrt (h/4.9)

Second time, h/343

so (h/343) + sqrt (h/4.9) = 3.50

(h/343) + sqrt (h/4.9) - 3.50 = 0

I would solve this graphically. Using Desmos or a graphing calculator plot

y = (x/343) + sqrt (x/4.9) - 3.50, then read off the x-intercept.