Answer: ok, so total time is Tt = 6.65 seconds = time falling + time of sound traveling.
the time of the rock falling is given by: [tex](g/2)*t₀^{2} -h = 0[/tex] (1)
where h is the heigth of the hole, and t₀ is the time it took to reach the bottom.
the time of the sound traveling is given by 343*t₁ - h = 0 (2)
so t₁ + t₀ = 6.65s = total time
then you know that t₁ = 6.65s - t₀
so now you have two variables, t₀ and h, and we want to know the value of h, so we want to write t₀ as a function of h.
in the second equation we have now: 343*(6.65 - t₀) = h
so t₀ = (-h/343 + 6.65)s
replacing this on the first equation you have:
[tex](g/2)*(-h/343 + 6.65)^{2} -h = 0[/tex]
now you want to take h to the right side so
w
so if we replace g by 9.8 meters over seconds square we get
h = [tex]\frac{-1.19 -+ \sqrt[2]{1.56} }{2*0.00041}[/tex]
where you will take the positive root
h = 61 meters
