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Applications of Horizontal and Vertical Components

A bomb of mas...

Question

A bomb of mass 3m is kept inside a closed box of mass 3m and length 4L at it's center. It explodes in two parts of mass m and 2m. The two parts move in opposite directions and stick to the opposite sides of the walls of box. The box is kept on a smooth horizontal surface. What is the distance moved by the box during this time interval ?

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Solution

$Δ X_{c m} = \frac{M_{1} Δ X_{1} + M_{2} Δ X_{2} + M_{3} Δ X_{3}}{M_{1} + M_{2} + M_{3}}$

$0 = 3 M X + 2 M (M + 2 L) + (X - 2 L)$

$6 M X = 2 M L - 4 M L$

$X = \frac{L}{3}$

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