Question

A body of mass $1kg$ initially at rest, explodes and breaks into three fragments of masses in the ratio $1:1:3$. The two pieces of equal mass fly-off perpendicular to each other with a speed of $30m/s$ each. What is the velocity of the heavier fragment?

Answer 1

Let $v$ be the velocity of third fragment $\left(\frac{3}{5}{k}_0\right).$

By momentum conservation,

$\Rightarrow V_x\left(\frac{3}{5}\right)-\frac{1}{5}\left(30\right)=0$

$\Rightarrow V_x=10m/s$

Similarly $V_y=10m/s$

$\Rightarrow V=\sqrt{V_x^2+V_y^2}$

$=10\sqrt{2}m/s.$

Hence, the answer is $10\sqrt{2}m/s.$