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 v₁.  The boy at A starts simultaneously with velocity y as shown in figure and catches the other boy in a time t, where t is

• A

  $\frac{\mathrm{a}}{\left(\mathrm{v}+{\mathrm{v}}_1\right)}$

• B

  $\frac{\mathrm{a}}{\sqrt{\left({\mathrm{v}}^2+{\mathrm{v}}_1^2\right)}}$

• C

  ${\left[\frac{{\mathrm{a}}^2}{\left({\mathrm{v}}^2-{\mathrm{v}}_1^2\right)}\right]}^{1/2}$

• D

  $\frac{\mathrm{a}}{\left(\mathrm{v}-{\mathrm{v}}_1\right)}$