Two boys are standing at the ends A and B of a ground where

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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, where t is

1. a / √v² + v₁²
2. a / (v + v₁)
3. a / (v - v₁)
4. √a² / (v² + v₁²)

Correct Option: D

Velocity of A relative to B is given by
V^{^→}_{A / B} = v^{^→}_A - v^{^→}_B = v^{^→} - v^{^→}₁ ......(1)
By taking x-components of equation (1), we get

0 = v sin θ - v₁ ⇒ sin θ =	v₁	.........(2)
	v

By taking Y-components of equation (1), we get
v_y = v cos θ ........(3)
Time taken by boy at A to catch the boy at B is given by

t =	Relative displacement along Y - axis
	Relative velocity along Y - axis

=	a	=	a
	v cos θ		v . √1 - sin² θ

[From equation (1)]