I read the answer of it, but I don't get why the answer is that.You forget to hold your gun against your shoulder and it recoils into you. How much Joules of kinetic energy end up in your shoulder? Assume you and the gun move together in the end.
masses: You=90 kg, gun=10kg, bullet= 0.0085kg
velocity of the bullet = 87m/s
And the answer is
1/2 M gun x (M bullet * V bullet / M gun)^2
- 1/2 M gun+you x (M bullet * V bullet/ M gun+you) ^2