Question

A bomb explodes into three fragments having masses in the ratio of $1:1:3$. Two fragments having masses in the ratio $1:3$ move at right angles to each other with a velocity of $15m/s$. Find the K.E of heavy fragment.

Answer 1

Let the masses be $1kg,1kg\&3kg$

Now, $\overrightarrow{P_1}+\overrightarrow{P_2}+\overrightarrow{P_3}=0$

$\overrightarrow{P_2}=-(\overrightarrow{P_1}+\overrightarrow{P_2})|\overrightarrow{P_2}|=\sqrt{P_1^2+P_2^2}=\sqrt{{15}^2+(3\times 15{)}^2}=\sqrt{225+2025}=\sqrt{2250}K.E=\frac{P^2}{2m}=\frac{2250}{2\times 1}=1125kg{m}^2/s^2$