Question

A rock is dropped from the surface into a pit. It hits the bottom of the pit in 5.0 seconds. A second rock is then dropped into a second pit, where it hits the bottom in 10 seconds. How much deeper is the second pit compared to the first pit? Neglect air resistance

Answer 1

The first pit is 125 meters deep while the second pit is 500 meters deep

Answer 2

Answer

second pit is 4 times deeper compared to the first pit.

Explanation

The first pit is 125 meters deep while the second pit is 500 meters deep

We know from second equation of motion

$s=ut+.5at^2$..........(1)

here s-depth of pit

u=0 (initial velocity0

a-gravitational acceleration (a=g=9.8m$s^{-2}$

t-time

when t=5second

put value of t,a and u in equation 1

$s_{1}=0+.5\times 9.8ms^{-2}\times 5^2s^2$

$s_{2}=122.5m$

similarly when t=10s

put value of t,a and u in equation 1

$s_{2}=0+.5\times 9.8ms^{-2}\times10^2s^2$

$s_{2}=490m$

therefore,

$\frac{s_{2}}{s_{2}}=\frac{490}{122.5}\\\frac{s_{2}}{s_{2}}=4$

It means second pit is 4 times deeper compared to the first pit.