Projectile Kinetic Energy and Recoil in Spring Gun Experiment

[CoreanJesus]

Homework Statement

A projectile of mass M1 is fired horizontally from a spring gun that is initially at rest on a frictionless surface. The combined mass of the gun and projectile is M2. If the kinetic energy of the projectile after firing is K, the gun will recoil with a kinetic energy equal to...

Homework Equations

this is part of the problem.
I know you need the kinetic energy formula but I don't get the other formula.

The Attempt at a Solution

N/A Answer is (M1/(M2-M1))K

 

[DoItForYourself]

Hi,

You will need to take into consideration that the total momentum is conserved.

 

[CoreanJesus]

But what should the initial momentum be? 0?

 

[DoItForYourself]

Yes, the initial momentum is zero. That does not mean that the final velocity of the gun and of the projectile will be also zero. Do not forget that velocity (and momentum too) is a vector. So if you have two velocities (or momentum) in the opposite directions, you need to subtract one velocity from the other.

 

[CoreanJesus]

so M1V1=(M2-M1)V2
K=.5M1V1^2
KE=.5(M2-m1)V2^2 and plugin?

 

[DoItForYourself]

Exactly.

 

[CoreanJesus]

Thank you so much!