boy throws a penny into an empty well with an initial velocity of –2 m/s. He hears it hit the bottom 8 seconds later. About how far did the penny fall?

Answer 1

t'=time to fall
t"=time for sound to return after bottom

t'+t"=8

depth=2*t'+1/2 g t'^2
depth=velocitysound*t"

set them equal (same depth)

2*t'+1/2 g t'^2=velocitysound*t"
2*t'+1/2 g t'^2=velocitysound*(8-t')

so solve for t', and then you can get depth.