# Recoil speed

1. Mar 14, 2015

### henry3369

1. The problem statement, all variables and given/known data
A hunter on a frozen, essentially frictionless pond uses a rifle that shoots 4.20g bullets at 950m/s . The mass of the hunter (including his gun) is 72.5kg , and the hunter holds tight to the gun after firing it.

Find the recoil speed of the hunter if he fires the rifle at 52.0∘ above the horizontal.

2. Relevant equations

3. The attempt at a solution
Vx = 950cos(52)
Vy = 950sin(52)

Conservation of Momentum in the x-Direction:
m1v1' = -m2v2'
(72.5)v1' = (-0.0042)(950cos(52))
v1' = -0.033882611 m/s

Conservation of Momentum in the y-Direction:
m1v1' = -m2v2'
(72.5)(v1') = (-0.0042)(950sin(52))
v1' = -0.043367764 m/s

vf = sqrt(0.0338826112+0.0433677642) = 0.055 m/s

The correct answer is 0.0339 m/s

What am I doing incorrectly?

2. Mar 14, 2015

### Staff: Mentor

Is the hunter free to recoil in the Y-direction?

3. Mar 14, 2015

### henry3369

I know that the hunter wouldn't move in the y-direction, but wouldn't there still be an initial velocity in the y-direction? Similar to how if an object is dropped, it has a y-component of velocity right as it hits the ground.

4. Mar 14, 2015

### Staff: Mentor

The hunter is already on the ice surface. Any velocity in the downward direction would have to include the ice and the rest of the planet.