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HARD Mechanics A-LEVEL Maths Question!!

In order to determine the depth of a well, a stone is dropped into the well and the time taken for the stone to drop is measured. It is found that the sound of the stone hitting the water arrives 5 seconds after the stone is dropped. If the speed of sound is 340ms-1. Find the depth of the well.

I am really stuck on this question....

Spoiler

(edited 6 years ago)

Reply 1

cheesecakelove

Speed = distance/time ?

Reply 2

Hilaryisme

The depth is equal to the speed of sound times the time taken by the sound:

340 m/s x 5 seconds

Reply 3

RogerOxon

Original post by Hilaryisme

The depth is equal to the speed of sound times the time taken by the sound:

340 m/s x 5 seconds

No.

5s is the time for the stone to drop and the sound to reach the top again.

Start with

s=\frac{gt^2}{2}

(from

s=u+\frac{at^2}{2}

) and

t=5-\frac{s}{340}

Reply 4

Intel_Imperator

You guys are really not smart. You can't do this without SUVAT. I'm in AS Level, so i'm not a master at this, but its the route you need to take.

Reply 5

gcse0

Has anyone actually got the answer to the question?
The answer is in the spoiler in the first post.

Reply 6

Squiidsquid

I've got the answer (if assuming the 'bottom' of the well is where the water is?)

Why do you need help if you've got the answer?

Reply 7

Kaiylar

Original post by Squiidsquid

I've got the answer (if assuming the 'bottom' of the well is where the water is?)

Why do you need help if you've got the answer?

Likely he doesn't know the method, just has access to the answer.

Reply 8

Squiidsquid

Equate the distance the rock falls and the distance the sound travels back up. You should get an equation linking the times taken for both scenarios. From there you can work out a value for one of the times, and then evaluate the answer from that?

Reply 9

RogerOxon

Original post by gcse0

Has anyone actually got the answer to the question?
The answer is in the spoiler in the first post.

Yes. The equations that I gave lead to that answer:

Original post by RogerOxon

Start with

s=\frac{gt^2}{2}

(from

s=u+\frac{at^2}{2}

) and

t=5-\frac{s}{340}

Reply 10

gcse0

Original post by RogerOxon

Yes. The equations that I gave lead to that answer:

Could you explain how you obtain the equation, like the maths behind it?

Reply 11

Bertybassett

Original post by gcse0

Could you explain how you obtain the equation, like the maths behind it?

and then it came to troy deeeennnnnnnnnnnnnnneyyyyyyyyyyyyyyyyyyyyyy

Reply 12

RogerOxon

Original post by gcse0

Could you explain how you obtain the equation, like the maths behind it?

s=\frac{gt^2}{2}, \therefore t^2=\frac{2s}{g}

\therefore (5-\frac{s}{340})^2=\frac{2s}{g}

Simplify and solve the quadratic, taking the positive solution. You can confirm this by substituting the answer in the first post's spoiler into the above - it works.

Reply 13

gcse0

Original post by RogerOxon

s=\frac{gt^2}{2}, \therefore t^2=\frac{2s}{g}

\therefore (5-\frac{s}{340})^2=\frac{2s}{g}

Simplify and solve the quadratic, taking the positive solution. You can confirm this by substituting the answer in the first post's spoiler into the above - it works.

Does g represent acceleration of the dropped object?

Reply 14

RogerOxon

Original post by gcse0

Does g represent acceleration of the dropped object?

Yes

The question is flawed as the presence of air resistance isn't made 100% clear.

Reply 17

HiggsBroson

Was the answer 107.5m

Reply 18

Sam Prior

I got 107.5m. Use simultaneous equations with both ideas of sound travelling up and the stone falling under constant acceleration. Find both in terms of s and t, and then solve

Reply 19

mqb2766

Original post by JC53

I stumbled on to this post today so I apologise for the late reply but here is the full solution

Its worth having a read of the forum guidelines
https://www.thestudentroom.co.uk/showthread.php?t=4919248
and not posting full solutions and not bumping 4 year old threads. Could you pls delete?