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=√((29)^2+(29)^2)=29\sqrt 2m/s`

b.
`\theta=tan^(-1)((v_y)/(v_x))=tan^(-1)((29)/(29))=45^(\circ)`

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