Collisions thought i was doing it right?

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In this discussion, a collision problem involving two rocks in space is presented, where the first rock has a mass of 4 kg and an initial velocity of <3900, -3000, 3200> m/s, and the second rock has a mass of 17 kg with an initial velocity of <300, -260, 260> m/s. After the collision, the first rock's velocity changes to <3500, -2300, 3700> m/s, and the goal is to find the final velocity of the second rock. The momentum conservation principle is highlighted, emphasizing that the total momentum before the collision equals the total momentum after the collision. The discussion clarifies that the final velocity of the two rocks will differ due to the nature of elastic collisions. The user seeks guidance on the correct method to solve for the final velocity of the second rock.
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In outer space a rock with mass 4 kg, and velocity < 3900, -3000, 3200 > m/s, struck a rock with mass 17 kg and velocity < 300, -260, 260 > m/s. After the collision, the 4 kg rock's velocity is < 3500, -2300, 3700 > m/s.
What is the final velocity of the 17 kg rock?

m1 = 4 kg
v1 = < 3900, -3000, 3200 > m/s

m2 = 17 kg
v2 = < 3500, -2300, 3700 > m/s



Attempt at a solution:

pf = pi1 + pi2

(m1 + m2)*vf = m1v1 + m2v2
...solve for v2

as i was typing this i realized one of my mistakes is that the left side isn't (m1 +m2) but I'm still not sure what this should be?

Thanks for the help!:-)
 
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It's an elastic collision so the two rocks will not necessarily be moving with the same velocity. You cannot assume that vf will be the velocity of both masses.
 
what method would i use to solve for v2f then?
 
Well if this is a closed system then the rocks masses will remain constant, so will the total momentum in the system, so we can see that m1vi1 + m2vi2 = m1vf1 + m2vf2

You have know m1, m2, vi1, vi2, vf1 you have one unknown...
 
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