You may ignore air resistance. How high is the building? The speed of sound is v_s.?

Question

A physics student with too much free time drops a watermelon from the roof of a building. He hears the sound of the watermelon going "splat" after a time interval of Delta(t)

You may ignore air resistance. How high is the building? The speed of sound is v_s.

Answer 1

The time it takes to hit the ground from eq x=xo+v0t+1/2 gt^2
is t^2=2h/g
and for the sound to reach you after impact is
t=h/v_s
so the total time T=h/v_s +sqrt(2h/g)
(T-h/v_s)^2=2h/g
T^2-2Th/v_s+(h/v_s)^2-2h/g=0

Use quadratic formula to solve for h