A stone falls freely under gravity. It covered distances `h_1, h_2` and `h_3` in the first `5` seconds. The next `5` seconds and the next `5` seconds respectively. The relation between `h_1, h_2` and `h_3` is :

Options

A. `h_1=h_2=h_3`
B. `h_1=2h_2=3h_3`
C. `h_1=(h_2)/(3)=(h_3)/(5)`
D. `h_2=3h_1` and `h_3=3h_2`

Answer

C

Explanation

`h_1=1/2g(5)^2=25/2g`
`h_2=1/2g(10)^2-1/2g(5)^2=75/2g`
`h_3=1/2g(15)^2-1/2g(10)^2=(125g)/2`
`h_1=(h_2)/3=(h_3)/5`