Calculus help

Swampy

Swampy

Member
I know this isn't a homework help site but I need help on this and it's due today before midnight, so if anyone is good with calculus could you help me out? Thanks.

You drop a rock into a well (from ground level). You can't see the impact at the bottom but you hear it after 7.9 seconds. You wonder how deep the well is. Assume the speed of sound is 1100 feet per second and the acceleration of the rock is 32 feet per second squared. Ignore air drag (this is a major simplifying assumption).

(Hint: the time till you hear the impact is the sum of the time the rock takes to reach the bottom and the time the sound of the impact takes to travel back to your ear.)

The depth of the well (in feet) is?

Gah, that speed of sound deal is confusing me
 
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
 
yeah I don't see how to solve it either, it gives you 7.9 seconds and 32ft/sec squared for gravity. So how do you find out how much time is actually falling, and how much time is the speed of sound, wtf? for the function what would I put the speed of sound as?
 
yeah my calculus teacher keeps saying over and over calculus is super easy once you get the hang of it. luckily he's my AP calculus and Physics 2 teacher so he ties it all in and it makes sense
 
If you must know

Uniform acceleration : ∆d = 1/2 a•t^2

Uniform motion: ∆d = v*t

so

Depth of the well = 1/2 32 *t1^2 = 1100*t2

Time = 7.9 = t1 + t2

2 equations, solve the quadratic to find the time to fall. Use the time to find depth.

819.173 feet
 
Fuck. Im taking grade 12 Data Management. But I dont need math concidoring I'm going into teaching for the Social Sciences.
 
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