A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by $1\,m/s$ so as to have same K.E. as that of the boy. The original speed of the man will be
A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by $1\,m/s$ so as to have same K.E. as that of the boy. The original speed of the man will be
$\sqrt 2 \,m/s$
$(\sqrt 2 - 1)\,m/s$
$\frac{1}{{(\sqrt 2 - 1)}}m/s$
$\frac{1}{{\sqrt 2 }}m/s$
A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by $1\,m/s$ so as to have same K.E. as that of the boy. The original speed of the man will be
Let m = mass of boy, $M =$ mass of man
$v =$ velocity of boy, $V =$ velocity of man
$\frac{1}{2}M{V^2} = \frac{1}{2}\left[ {\frac{1}{2}m{v^2}} \right]$…..(i)
$\frac{1}{2}M{(V + 1)^2} = 1\left[ {\frac{1}{2}m{v^2}} \right]$…..(ii)
Putting $m = \frac{M}{2}$ and solving $V = \frac{1}{{\sqrt 2 - 1}}$
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