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weirdlycool
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Homework Statement
Consider a gun of mass M (when unloaded) that fires a shell of mass m with muzzle speed v. (That is, the shell's speed relative to the gun is v.) Assuming that the gun is completely free to recoil (no external forces on gun or shell), use conservation of momentum to show that the shell's speed relative to the ground is ##\frac{v}{(1+ \frac{m}{M})}##
Homework Equations
##p=mv##
##m_1 v_1 = m_2 v_2##
##M = ## mass of the gun
##m = ## mass of the shell
##v = ## speed of the shell relative to the gun's muzzle
##v_g = ## shell's speed relative to the ground
The Attempt at a Solution
##p_{initial} = Mv##
##p_{final} = ( M + m ) v_g##
I'm not sure if the initial and final momentum is correct
##Mv = ( M + m ) v_g##
##v = (1 + \frac{m}{M}) v_g ##
##v_g = \frac{v}{(1+ \frac{m}{M})}##
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