How Do You Calculate Recoil Speed in Ballistics?

[Ki-nana18]

A bullet with mass 0.40 kg is fired with an initial velocity of 400 m/s from a gun with mass 5.0 kg. The speed of the recoil of the gun is?

Do I use this equation m₁v₁=m₂v₂?
Can someone give me just a hint?

 

[rock.freak667]

Yes you would need to use conservation of linear momentum.

 

[tomcue]

Yes, to calculate the speed of recoil, we can use the conservation of momentum equation, which states that the total momentum before an event is equal to the total momentum after the event. In this case, the initial momentum of the bullet and gun before firing is equal to the final momentum of the bullet and gun after firing.

So, we can set up the equation as m1v1 = m2v2, where m1 is the mass of the bullet, v1 is the initial velocity of the bullet, m2 is the mass of the gun, and v2 is the final velocity of the gun after firing.

Substituting the given values, we get (0.40 kg)(400 m/s) = (5.0 kg)(v2).

Solving for v2, we get v2 = 32 m/s.

Therefore, the speed of recoil for the gun is 32 m/s. Keep in mind that this is the magnitude of the velocity, so the direction of the recoil would be opposite to the direction of the bullet's velocity.