Recoil velocity, please help?

Question

Alright, here is the question. I'll tell you how far I've gotten trying to figure it out.

"A rifle with a weight of 40 N fires a 5.0 g bullet with a speed of 230 m/s.
(a) Find the recoil speed of the rifle.
(b) If a 600 N man holds the rifle firmly against his shoulder, find the recoil speed of the man and rifle."

The formula I've been attempting to use for recoil velocity of the rifle is m1v1(i) + m2v2(i) = m1v1(f) + m2v2(f)

Wouldn't the entire left side be equal to zero, as both the initial velocity of the rifle and the bullet are zero?

On the right side, I've plugged in m1 = 40N, v1 = ?, m2 = .005 kg (mass of bullet conv. to kg), and v2 = 230 m/s. Solving for v1(f) where the left side has a value of 0, I get the answer -.02875 m/s (recoil velocity of the rifle). This is coming back wrong. What am I missing? Am I even using the right formula? Thanks!

- .2875 is the answer I'm getting. The negative sign in the question got cut off.

Bah, typo. -.02875 m/s.

Answer 1

This question could be phrased better, but as is, I'd use a simlar equation: m1v1=m2v2, using the 2 known masses and one known velocity. 5g is a mass, and convert 40N (and later, 600N) into kg by dividing by gravity (so 40N/9.8m/s/s = 4.08kg, etc).

I get .28 m/s using that equation. I think it's right.

Answer 2

1) weight of 40 N means the mass is 4 kg.
mv + MV = 0
4*v = -5/1000 * 230
v = -5 *230 / 4000
v = -0.2875 m/s
This isn't wrong its correct. -ve sign indicates that the recoil is in opposite direction of the motion of bullet.

2) (m+man)v = - MV
(60 + 4)v = - 5 * 230 / 1000
v = -5*230 / 6400
v = -0.1796 m/s
This is the recoil speed of the man plus rifle
if u want to find the recoil of the man and rifle individually then this velocity will be divided between the two inversely in the ratio of their masses. that is , the one with more mass will have less velocity and vice versa.

Answer 3

40/9.8* v1-0.005 *230 =0
so v1= 0.005 *230/40 *9.8=0.282m/s
Now instead of 40/9.8 you have a mass of 640/9.8 kg
You are right.,the left side is zero but momentum is a vector so don´t forget the direction