Question

A vessel at rest explodes breaking it into three pieces. Two pieces having equal mass fly off perpendicular to one another with the same speed of $30m/s$. The third piece has three times the mass of each other piece. What is the magnitude and direction of its velocity( magnitude in m/s) immediately after the explosion:

• A. $10\sqrt{2},{135}^{\circ }$
• B. $10\sqrt{2},{90}^{\circ }$
• C. $10\sqrt{2},{60}^{\circ }$
• D. $10\sqrt{2},{30}^{\circ }$

Answer 1

The correct option is A $10\sqrt{2},{135}^{\circ }$

Let v be the velocity of $3^{rd}$ piece according to figure
$3mv\cos \theta =mu$ and $3mv\sin \theta =mu$
$\Rightarrow \tan \theta =1\Rightarrow \theta ={45}^{\circ }$
$\therefore 3mv=\sqrt{2}mu$
$\Rightarrow v=\frac{30\sqrt{2}}{3}=10\sqrt{2}$
As seen from the figure, the third piece is inclined at ${135}^{\circ }$ w.r. t direction of each one.