Discussion Forum



1)

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


A) $\sqrt{2}$m/s

B) $\sqrt{2} -1$m/s

C) $\frac{1}{(\sqrt{2}-1)}$

D) $\frac{1}{(\sqrt{2})}$

Answer:

Option C

Explanation:

Let m = mass of boy, M = mass of man v = velocity of boy, V = velocity of man,

$\frac{1}{2}MV^{2} = \frac{1}{2}\left[\frac{1}{2}mv^{2}\right]$ ...(i)

$\frac{1}{2}M(V+1)^{2} = 1\left[\frac{1}{2}mv^{2}\right]$ ....(ii)

Putting m = M/2 and  solving V= $\frac{1}{\sqrt{2}-1}$