Momentum/kinetic energy w/ rifle

[CollegeStudent]

Homework Statement

A rifle with a mass of 3.22 kg fires an 11.9 g bullet at a velocity of 590 m/s. What is the recoil velocity of the rifle? Compare the change in momentum of the bullet and the rifle. Compare the change in kinetic energy of the bullet and the rifle. Which is bigger, by what factor?

Homework Equations

m_1v_1 + m_2v_2 = m_1v_1 + m_2v_2
(initial) (final)

K = 1/2mv²

The Attempt at a Solution

(a)What is the recoil velocity of the rifle?

We know

mass of rifle = 3.22 kg
mass of bullet = .0119 kg
initial velocity of rifle = 0
initial velocity of bullet = 0 (this one I thought would be the 590m/s but my prof said they both start from rest)
final velocity of bullet = 590 m/s
final velocity of rifle = V_1 (what we want)

m_1v_1(initial) + m_2v_2(initial) = m_1v_1(final) + m_2v_2(final)


So this would be solving for v_1 final so rearrange for that

V_1 = [m_1v_1(initial) + m_2v_2(initial) - m_2v_2(final)]/ m_1

V_1 = [3.22 kg(0) + .0119 kg(0) - .0119 kg(590m/s)] / 3.22 kg
(the answer would be a negative number which makes sense because the direction is opposite)

so V_1 = -2.18m/s


(b) Compare the change in momentum of the bullet and the rifle.

I'm not sure about this one


(c) Compare the change in kinetic energy of the bullet and the rifle

I was thinking

1/2mV_f² - 1/2mV_i² for the bullet and for the rifle

so

mass of rifle = 3.22 kg
mass of bullet = .0119 kg
initial velocity of rifle = 0
initial velocity of bullet = 0 (this one I thought would be the 590m/s but my prof said they both start from rest)
final velocity of bullet = 590 m/s
final velocity of rifle = V_1 (what we want)

Rifle

ΔK_r = 1/2mV_f² - 1/2mV_i²
= 1/2(3.22kg)(-2.18m/s)² - 1/2(3.22kg)(0)²

K_r = 7.65J


Bullet

ΔK_b = 1/2mV_f² - 1/2mV_i²
= 1/2(.0119 kg)(590 m/s)² - 1/2(.0119 kg)(0)²

K_b = 2071.2J



Are these correct? and how would I go about (b)? I'm just not too sure what it is asking

 

[CWatters]

The change in momentum of each is calculated much like you did for the change in KE eg...

mV_f - mV_i

 

[CollegeStudent]

The change in momentum of each is calculated much like you did for the change in KE eg...

mV_f - mV_i

Oh...I thought I had to go through all of the
m_1v_1 + m_2v_2 = m_1v_1 + m_2v_2
again...and I didn't get what I would be solving for


Okay so

change in momentum of Rifle

3.22(-2.18m/s) - 3.22kg(0) = -6.5836
(only negative to show direction)

change in momentum of Bullet

.0119(590) - .0119(0) = 7.021

Is that correct?