i briefly looked at this problem and i'm struggling with this speed of sound deal as well. but i'll throw out what i'm thinking to see if it will help
i'm only 17 so dont' hate me if i get this really wrong
i'm looking at this more of a physics problem. immeditatly i used 9.8 m/s2 as acceleration rather than 32 feet/s2. metric is so much easier with math.
i set it up like any basic physics problem using the 5 variables to solve for
initial velocity - Vo
final velocity - Vf
displacement - s
acceleration - a
time - t
you have initial velocity as 0 m/s because its from rest
a is 9.8 m/s2 or the pull of gravity because luckily air resistance is neglected.
i'm sure you got here. and probably like you i'm stuck with the whole speed of sound thing. once you know the time it took to fall to the water you're golden. so its 1100 f/s or 335.28 m/s. and you hear the splash after 7.9 seconds
so first the equation Ti = Tb + Tsi (time till you hear impact = time to bottom + time the sound takes to get to you). untill i can figure out how to solve that i don't know whats next.
wow i don't know how to solve this. sorry for wasting space but maybe if i talk through this it can help me and you. if i go on 7.9 seconds is time to reach bottom then speed at the bottom is 77.42 m/s and displacement is 305.809 feet. i just can't see where to go, or if that even is necessary because 7.9 seconds is time till you hear, not time till impact.
i don't see how this is possible to solve, considering you can't figure out how much time it takes till you hear the drop until you know how deep the well is. and you can't find out how deep the well is until you figure out how long the sound took to reach you
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