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 running simultaneously with velocity 𝑣 and catches the other boy in a time 𝑡, when 𝑡 is

Question : 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 running simultaneously with velocity 𝑣 and catches the other boy in a time 𝑡, when 𝑡 is

(A) \dfrac{a}{\sqrt{\left[ v^{2}+V_{1}^{2}\right] }}

(B) \sqrt{a^{2}/\left( V^{2}-V_{1}^{2}\right) }

(C) a/\left( v+v_{1}\right)

(D) a/\left( v-v_{1}\right)

Answer : option (B)

Solution :

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 running simultaneously with velocity 𝑣 and catches the other boy in a time 𝑡, when 𝑡 is
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