Question

A running man has the same kinetic energy as that of a boy of half his mass. The man speeds up by $2\text{m/s}$ and the boy changes his speed by $x\text{m/s}$ so that the kinetic energies of the boy and the man are again equal. Then $x$ in $\text{m/s}$ is

• A. $3\sqrt{2}$
• B. $2\sqrt{2}$
• C. $\sqrt{2}$
• D. $2$

Answer 1

The correct option is B $2\sqrt{2}$

Let $m$ be mass of the man, $v_m$ be speed of the man and
$m/2$ be mass of the boy, $v_b$ be speed of the man
Initially, KE of man = KE of boy
$\frac{1}{2}m{v}_m^2=\frac{1}{2}\left(\frac{m}{2}\right)v_b^2\Rightarrow v_b=\sqrt{2}{v}_m$
In the second case,
$\frac{1}{2}m(v_m+2{)}^2=\frac{1}{2}\left(\frac{m}{2}\right)(v_b+x{)}^2$
$\Rightarrow v_m+2=\frac{1}{\sqrt{2}}[v_b+x]=\frac{1}{\sqrt{2}}[\sqrt{2}{v}_m+x]$
$\Rightarrow v_m+2=v_m+\frac{x}{\sqrt{2}}$
$\Rightarrow \frac{x}{\sqrt{2}}=2\Rightarrow x=2\sqrt{2}$
Hence, the correct answer in option (b).