Question

A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by 1m/s so as to have same K.E. as that of the boy. The original speed of the man will be

Moderate

Solution

Let m = mass of boy, M = mass of man
v = velocity of boy, V = velocity of man
$\frac{1}{2} {MV}^{2} = \frac{1}{2} [\frac{1}{2} {mv}^{2}]$ …..(i)
$\frac{1}{2} M {(V + 1)}^{2} = 1 [\frac{1}{2} {mv}^{2}]$ …..(ii)
Putting $m = \frac{M}{2}$ and solving $V = \frac{1}{\sqrt{2} - 1}$

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