Relative Motion in Two Dimensions

2005 AIPMT 1 question

1. 1 Motion in a Plane
   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 -
   A $\dfrac{a}{\sqrt{v^2 + v_1^2}}$ B $\sqrt{\dfrac{a^2}{v^2 - v_1^2}}$ C $\dfrac{a}{(v - v_1)}$ D $\dfrac{a}{(v + v_1)}$
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