Question

A physics student with a stopwatch drops a rock into a very deep well, and measures the time between when he drops the rocks and when he hears the sound of the rock hitting the water below. If the speed of sound is 343 m/s, and the student measures a time of 6.20 s, how deep is the well?

Answer 1

Answer:

h= 161.06 m

Explanation:

Given that

Speed of the sound ,C= 343 m/s

Total time ,t= 6.2 s

lets take the depth of the well = h

The time taken by stone before striking the water = t₁

we know that

$h=\dfrac{1}{2}gt_1^2$

$t_1=\sqrt{\dfrac{2h}{g}}$

The time taken by sound =t₂

$t_2=\dfrac{h}{343}$

The total time

t = t₁+ t₂

$6.2 = \sqrt{\dfrac{2h}{g}}+\dfrac{h}{343}$

$6.2 = \sqrt{\dfrac{2h}{9.81}}+\dfrac{h}{343}$

Now by solving the above equation we get

h= 161.06 m

Therefore the depth of the well will be 161.06 m.