Explanation

(c) Consider the two cart system as a single system. Due to explosion of power charge total momentum of system remains unchanged $ie,$ ${\overrightarrow{p}}_{1} + \ {\overrightarrow{p}}_{2} =$ or $m_{1}v_{1} = m_{2}v_{2}$,
Hence
$\frac{v_{1}}{v_{2}} = \frac{m_{2}}{m_{1}}$
As coefficient of friction between carts and rails are identical, hence $a_{1} = a_{2}$ and at the time of stopping final velocity of cart is zero. Using equation $v^{2} - u^{2} = 2as$,
We have
$\frac{s_{1}}{s_{2}} = \frac{v_{1}^{2}}{v_{2}^{2}} = \frac{m_{2}^{2}}{m_{1}^{2}} \Rightarrow s_{2} = \frac{s_{1}m_{1}^{2}}{m_{2}^{2}} = \frac{36 \times (200)^{2}}{(300)^{2}} = 16$m