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

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

Step-by-step 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* 9.8ms^(-2)* 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* 9.8ms^(-2)*10^2s^2`

`s_(2)=490m`

therefore,

`(s_(2))/(s_(2))=(490)/(122.5)\\(s_(2))/(s_(2))=4`

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