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 velocity `v_(1)`. The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is :

Options

A. `a // sqrt(v^2 + v_1^2)`
B. `sqrt(a^2//(v^2 -v_1^2))`
C. `a//(v - v_1)`
D. `a// (v+v_1)`

Answer

B

Explanation

In `DeltaABC`
`(vt)^2 = a^2 + (v_1t)^2`
`t = sqrt((a^2)/(v^2 -v_1^2))`