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 $30 \,m/s$. The third piece has three times the mass of each other piece. What is the direction (w.r.t. the pieces having equal masses) and magnitude of its velocity 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

Answer: (A)

Suppose $m$ be the mass of each piece, flying off perpendicular to one another with same speed $u(=30\,ms^{-1})$ Then $3 \,m$ is the mass of the third piece Let $V$ be the velocity of $3^{rd}$ piece According to figure

$3mv \,cos\,\theta=mu$,
$3mv\,sin\,\theta=mu$
$tan\,\theta =1$ or $\theta=45^{\circ}$
$tan\,\theta =1$ or $\theta=45^{\circ}$
or $\frac{3v}{\sqrt{2}}=u=30\, m/ s$
or $v=10\sqrt{2}\, ms^{-1}$
(inclined at $135^{\circ}$ w.r.t. direction of each one)