How do I solve for height in this physics problem?

Question

1. You drop a quarter into a wishing well and hear the splash of the quarter 3.00 seconds after it is dropped. How deep is the well? The speed of sound at standard conditions is around 340 m/s.

Answer 1

Max

Well if the height is h m.

s = ut + 0.5 a t²

so to fall h metres, time will be sqrt (2h/a) where a = 9.8 m/s/s (u=0)

Then the sound has to travel back from the bottom of the well, taking h / 340 seconds

So sqrt (2h / 9.8) + (h/340) = 3, or sqrt (2h/9.8) + (h/340) - 3 = 0

So you can plot this on a graphing calculator or Desmos and find the zero

Mike