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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 answer: a/√v² + v₁²

Solution

The boy at A must run along the resultant of the two velocities to catch the boy at B. Using the Pythagorean theorem, the relative velocity between the two boys is √(v² + v₁²). The time taken to cover the distance 'a' is t = a / √(v² + v₁²).

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