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Hello everyone. First post here. I'll go the question straightaway.

A gun of mass "M" placed on a smooth horizontal surface fires a bullet of mass "m" with a velocity "u" at an angle "θ" with the horizontal (ground). The velocity of the center of mass of the gun+bullet system after firing is (in terms of M,m,u and θ)?

I know the velocity of the center of mass is given by the equation

v = mv / m

I expanded the above equation to V = (Mv1 + mv2)/(M+m), where v2 and v1 are the velocities of masses M and m after firing.

However, I do not know what values to substitute for v1 and v2. I substituted v2 to be ucosθ as it is along the horizontal, and then used the conservation of linear momentum principle to get v1=-mucosθ/M

substituting these values if the original formula, I got a wrong answer. The final answer is supposed to be

musinθ/(M+m)

What mistake have I done here? Thanks in advance for explaining.

## Homework Statement

A gun of mass "M" placed on a smooth horizontal surface fires a bullet of mass "m" with a velocity "u" at an angle "θ" with the horizontal (ground). The velocity of the center of mass of the gun+bullet system after firing is (in terms of M,m,u and θ)?

## Homework Equations

I know the velocity of the center of mass is given by the equation

v = mv / m

## The Attempt at a Solution

I expanded the above equation to V = (Mv1 + mv2)/(M+m), where v2 and v1 are the velocities of masses M and m after firing.

However, I do not know what values to substitute for v1 and v2. I substituted v2 to be ucosθ as it is along the horizontal, and then used the conservation of linear momentum principle to get v1=-mucosθ/M

substituting these values if the original formula, I got a wrong answer. The final answer is supposed to be

musinθ/(M+m)

What mistake have I done here? Thanks in advance for explaining.

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