Question

a stone is dropped in a well of depth 500 metres and a sound is heard after 45/4 seconds then speed of sound is (if gravity = 10m/s^2)




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Answer 1

Answer:

Split the problem into two parts:

stone falling depth = d

sound travelling up the well a distance = d

Use one of Newton’s equations of motion to solve for time to fall a distance = d:

S=Vit+12at2

I choose the sign convention: up=positive, down=negative

S=−d=−500,Vi=0,a=−10ms2

−500=12(−10)t2down

tdown=2(500)10−−−−−√=100−−−√=10sec

We can still use the same Newton’s equation of motion to solve for time for the sound to reach the top of the well:

S=Vit+12at2

but S=500,Vi=c,a=0

S=Vit

or

500=c(tup)

or

tup=500c

Total time t=tdown+tup=10+500c

but c=x∗102

∴ Total time = 454=10+500x∗102

x=4

The speed of sound in 20∘ air is 343 m/s, so my answer of c = 400 m/s looks reasonable.

Answer 2

Answer:

400 m/s

Explanation:

Time taken by stone to reach bottom of the well

=

$\sqrt{ \frac{2h}{g} } = \sqrt{ \frac{2 \times 500}{10} } = 10 \: seconds$

Time taken by sound to travel 500 m

=

$\frac{45}{4} - 10 = \frac{45 - 40}{4} = \frac{5}{4} s$

So speed

=

$\frac{500}{ \frac{5}{4} } = 400 \frac{m}{s}$