Two boys are standing at the ends A and B of a ground where AB = 'a'. The boy at B starts running in a direction perpendicular to AB with a velocity The boy at A also starts running simultaneously with velocity v in straight line and catches the B in time then t is :

Options

A. `a/sqrt(v^(2)+v_(1)^(2))`
B. `a/(v+v_(1))`
C. `a/(v-v_(1))`
D. `sqrt(a^(2)/(v^(2)-v_(1)^(2)))`

Answer

D

Explanation

Here as is clear from the fig.
`(v_(1)t)^(2) + a^(2)=(vt)^(2)`or `a^(2)=t^(2)(v^(2)-v_(1)^(2))`
`:.t=sqrt(a^(2)/(v^(2)-v_(1)^(2)))`