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Standard XII

Mathematics

Definition of Limit

Two boys are ...

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 $v_{1}$ . The boy at A starts running simultaneously with velocity $v$ and catches the other boy in a time t, where t is

\frac{a}{\sqrt{v^{2} + v_{1}^{2}}}

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\sqrt{\frac{a^{2}}{v^{2} - v_{1}^{2}}}

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\frac{a}{(v - v_{1})}

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\frac{a}{(v + v_{1})}

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Solution

The correct option is C $\sqrt{\frac{a^{2}}{v^{2} - v_{1}^{2}}}$
If boy A catches boy B in time t,
$⟹ (v t)^{2} = (v_{1} t)^{2} + a^{2}$
$⟹ t^{2} = \frac{a^{2}}{v^{2} - v_{1}^{2}}$
$⟹ t = \frac{a}{\sqrt{v^{2} - v_{1}^{2}}}$

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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

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