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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 in a time t, where t is

Asked in NEET 2005 · Relative velocity of two moving bodies

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

Step-by-step solution

Why the other options are wrong

• (1) Adds the squares where the geometry subtracts them. The catcher's displacement is the hypotenuse, so v²t²=a²+v₁²t² and the v₁² moves to the left-hand side.
• (2) Treats the two as approaching head-on along AB. They are not: one runs perpendicular to AB.
• (3) Treats it as a one-dimensional chase along AB, again ignoring that the runner leaves that line at once.

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