A body falls from a large height. The ratio of distance traveled in each time interval `t_(0)` during `t=0` to `t=3 t_(0)` of the journey is

Options

A. `1:4:9`
B. `1:2:4`
C. `1:3:5`
D. `1:2:3`

Answer

C

Explanation

`h_(1)=1/2g t_(0)^(2) …(i)`
`h_(1)+h_(2)=1/2 g(2t_(0))^(2) …(ii)`
`h_(1)+h_(2)+h_(3)=1/2 g(3t_(0))^(2) …(iii)`
`h_(2)=1/2g(3t_(0)^(2))`
`h_(3)=1/3g(5t_(0)^(2))`
`h_(1):h_(2):h_(3)=1:3:5`