Question

A running man has half the kinetic energy of a boy of half his mass. The man speeds up by 1 $m/s$ and then has the same kinetic energy as the boy . The original speed of the boy was:

• A. $2m/s$
• B. $9.8m/s$
• C. $4.8m/s$
• D. ​​​​​$7.2m/s$

Answer 1

The correct option is C $4.8m/s$

If original speed of a boy is $v_0$, then
$\frac{1}{2}M{v}^2=\frac{1}{4}\left[\frac{M}{2}{v_0}^2\right]$.....(i)

Also $\frac{1}{2}M(v+1{)}^2=\frac{1}{2}[\frac{M}{2}{v_0}^2]$......(ii)

From equation (i) and (ii),
$(\frac{v+1}{v}{)}^2=2$
$\Rightarrow v=\frac{1}{\sqrt{2}-1}$
$\Rightarrow v=\sqrt{2}+1$
From equation (i), $v_0=2v=4.8m/s$.