John Taylor Classical Mechanics Chapter 3, Problem 1

[karmonkey98k]

John Taylor "Classical Mechanics" Chapter 3, Problem 1

Homework Statement

Consider a gun of mass M (when unloaded) that fires a shell of mass m with muzzle speed v. (shell's speed relative to gun is v). Assuming gun is completely free to recoil (no ext. forces on gun or shell), use conservation of momentum to show that shell's speed relative to ground is v/(1+m/M)

Homework Equations

Pinitial=m1v1+m2v2 Pfinal=m1v + m2v=(m1+m2)v vfinal=(m1v1+m2v2/(m1+m2)

The Attempt at a Solution

I got v/(m/M), not the "+1

 

[haruspex]

P_final=m₁v + m₂v

The gun and shell are not moving together after firing.
Btw, this is the wrong forum. Should be in introductory physics.