A body is dropped from a height of 125 m. If = 10 `ms^(-2)` what is the ratio of the distances travelled by it during the first and last second of its motion :

Options

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

Answer

b

Explanation

`T=sqrt(2h)/(g)=sqrt((2xx125)/(10))=5s`
During first second the body falls through a height
`h_(1)=(1)/(2)g t_(1)^(2)=(1)/(2)xx101^(2)=5m`
During first four second the body falls through height
`h_2=(1)/(2) "gt"_(2)^(2)=(1)/(2)xx10xx4^(2)=80 m`
`:.` height through which the body falls in 5th second is `h_(3)`=125-80=45 m
`:.` `(h_(1))/(h_3)=(5)/(45)=(1)/(9)`