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A gun of mass M fires a bullet of mass m with a kinetic energy E. The velocity of recoil of the gun is?

A gun of mass M fires a bullet of mass m with a kinetic energy E. The velocity of recoil of the gun is?
 

Grade:11

3 Answers

Susmita
425 Points
5 years ago
Gun and bullet were at rest initially.So initial momentum was zero.That means final momentum of the system must be zero.Let v be velocity of bullet and V be that of gun.
So MV+mv=0
Or,V=-mv/M
Kinetic energy of bullet
E=(1/2)*mv2
or,v=root(2E/m)
So V=-(m/M)*root(2E/m)
Please approve if helped.
Arun
25750 Points
5 years ago
Momentum before firing = 0 
Momentum after firing = mv + MV

According to law of conservation of momentum, 

mv + MV = 0
Recoil velocity V = - mv /M
Aswanth
18 Points
5 years ago
 
Gun and bullet were at rest initially.So initial momentum was zero.That means final momentum of the system must be zero.Let v be velocity of bullet and V be that of gun.
So MV+mv=0
Or,V=-mv/M
Kinetic energy of bullet
E=(1/2)*mv2
or,v=root(2E/m)
So V=-(m/M)*root(2E/m)

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