Velocity of bullet relative to its mirror image after firing

[DriggyBoy]

A gun of mass 'M' fires a bullet of mass 'm' with a horizontal velocity 'v'. The gun is fitted with a plane mirror facing towards the receding bullet. Find the velocity relative to its image just after the gun is fired.

 

[Orodruin]

The above is simply the problem statement. What are your thoughts on the problem? Where do you get stuck?

 

[DriggyBoy]

Cannot proceed much...law of conservation of momentum needs to be applied i guess

 

[adjacent]

Cannot proceed much...law of conservation of momentum needs to be applied i guess

So apply it and show what you get.

 

[DriggyBoy]

I have solved but not sure if its correct. I have considered the velocity of the gun to be M. Now by conservation of linear mmntum, mv=MV...therefore V = mv/M
relative velocity wrt gun = v + V = mv/V + v = (m/M + 1)v
Therefore relative vel wrt image = 2*v(m/M + 1) = 2v(m/M + 1) [ since image dist = objct dist for plane mirror ]
Not sure...just check it...thanks in advance :)

 

[NascentOxygen]

That's the general idea, but you would lose marks for lack of rigor (and multiple typos!).

mv = -MV