A ball falls freely from rest. The ratio of the distance travelled in first, second, third and fourth second is

Options

A. `sqrt(2)-1`
B. `sqrt(2)+1`
C. `sqrt(2)`
D. None of these

Answer

B

Explanation

`1=(1)/(2)g t_(1)^(2)` or `t_(1)=sqrt((2)/(g))`
`2=(1)/(2)g t^(2)` or `t=sqrt((4)/(g))`
but `t_(2)=t-t_(1)=sqrt((4)/(g))-sqrt((2)/(g))`
`therefore (t_(1))/(t_(2))=(sqrt(2//g))/(sqrt(4//g)-sqrt(2//g))=(sqrt(2))/(2-sqrt(2))`
`=(sqrt(2)(2+sqrt(2)))/(2)=(sqrt(2)+1)`