Two boys are standing at 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 v$_1$. The boy at A starts running simultaneously with velocity v and catches the other boy in a boy in a time t. Calculate t in terms of a, v and v$_1$.

Question

$\begin{array}{1 1} \sqrt {\large\frac{a^2}{v^2+v_1^2}} \\ \sqrt {\large\frac{a^2}{v^2-v_1^2}} \\a^2\sqrt {\large\frac{v^2}{v^2-v_1^2}} \\ a^2\sqrt {\large\frac{v^2}{v^2+v_1^2}}\end{array}$