How deep is the well?

Jill drops a stone down a well and hears the splash from the bottom after 2.08 seconds.

Given that sound travels at a constant speed of 327 m/s and that the acceleration due to gravity is 9.8 m/s^2, how deep is the well?

Give you answer to the nearest metre.


The answer is 20.

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2 solutions

Zakir Dakua
Oct 25, 2015

S = 1 2 × g × t 2 \frac{1}{2} \times g \times t^{2} = 327 × ( 2.08 t ) 327 \times (2.08-t)

We get t = 2.02

So S = 1 2 × g × t 2 \frac{1}{2} \times g \times t^{2} = 1 2 × 9.8 × 2.0 2 2 \frac{1}{2} \times 9.8 \times 2.02^{2} = 20

Gery Wahyu
Oct 25, 2015

First we need to write the equation for the time

t 1 + t 2 = 2.08 t_1 + t_2 = 2.08 second

Where t 1 t_1 is equal to the time it takes for the stone to hit the bottom of the well and t 2 t_2 is equal to the time it takes for the sound to travel to Jill's ear.

From that we can use the equation

s = V o × t + 1 2 × g × t 2 s = V_o \times t + \frac {1}{2} \times g \times t^2 to solve t t

In which

t 1 t_1 will be equal to 2 s g \sqrt {\frac {2s}{g}}

And t 2 t_2 will be equal to s v \frac {s}{v}

Finally we get

2 s g + s v = 2.08 \sqrt {\frac {2s}{g}} + \frac {s}{v} = 2.08 second

Using algreba we find the answer = 20 meter

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