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?

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lublana lublana · Answer 1 · 2020-04-03T09:05:12+02:00

Answer with Explanation:

We are given that

[tex]m_1=m_2=m[/tex]

[tex]v_1=-29 im/s[/tex]

[tex]v_2=-29 jm/s[/tex]

[tex]m_3=3m[/tex]

a.Initial velocity of vessel,u=0

According to law of conservation of momentum

[tex]Mu=m_1v_1+m_2v_2+m_3v_3[/tex]

Where M=Mass of vessel

[tex]0=m(-29i)+m(-29j)+3mv_3[/tex]

[tex]29im+29jm=3mv_3[/tex]

[tex]v_3=29i+29j[/tex]m/s

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

b.[tex]\theta=tan^{-1}(\frac{v_y}{v_x})=tan^{-1}(\frac{29}{29})=45^{\circ}[/tex]

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