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

Question

Dr. Abubacker · Accepted Answer

(c) Let $m =$ mass of boy, $M =$ Mass of man
$v = \ $velocity of boy$,\ V = \ $velocity of man
$\frac{1}{2}MV^{2} = \frac{1}{2}\left\lbrack \frac{1}{2}mv^{2} \right\rbrack$ …(i)
$\frac{1}{2}M(V + 1)^{2} = 1\left\lbrack \frac{1}{2}mv^{2} \right\rbrack$ …(ii)
Putting $m = \frac{M}{2}$ and solving $V = \frac{1}{\sqrt{2} - 1}$

Q. 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

Explanation

Reviewed by Dr. Abubacker

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