Question

A vessel at rest at the origin of an xy coordinate system explodes into three pieces. Just after the explosion, one piece, of mass m, moves with velocity (-29 m/s) and a second piece, also of mass m, moves with velocity (-29 m/s) . The third piece has mass 3m. Just after the explosion, what are the (a) magnitude and (b) direction (as an angle relative to the +x axis) of the velocity of the third piece?

Answer 1

Answer with Explanation:

We are given that

$m_1=m_2=m$

$v_1=-29 im/s$

$v_2=-29 jm/s$

$m_3=3m$

a.Initial velocity of vessel,u=0

According to law of conservation of momentum

$Mu=m_1v_1+m_2v_2+m_3v_3$

Where M=Mass of  vessel

$0=m(-29i)+m(-29j)+3mv_3$

$29im+29jm=3mv_3$

$v_3=29i+29j$m/s

Magnitude,$\mid v_3\mid=\sqrt{(29)^2+(29)^2}=29\sqrt 2m/s$

b.$\theta=tan^{-1}(\frac{v_y}{v_x})=tan^{-1}(\frac{29}{29})=45^{\circ}$

Hence, direction of the velocity of third piece=45 degree