# 2D Momentum Problem

1. ### Probie1

38
1. The problem statement, all variables and given/known data

Car 1 weighing 1000 kg crashes into the rear of parked car 2 weighing 1100 kg and stops. Car2 moves ahead 2 ms2. What is the velocity of car1 at impact?

2. Relevant equations

(m1v1+m2v2)=(m1v3+m2v4)

3. The attempt at a solution

(m2V4)/m1
(1100*2)/1000
2.2ms2= 2200/1000

Okay, now I know this is right, but what I don't know is how do they arrive at the equation (m2v4)/m1 ????

2. ### Steely Dan

317
If you examine your original conservation of momentum equation, let $v_1, v_3$ be the initial and final speeds of car 1, respectively, and let $v_2,v_4$ be the initial and final speeds of car 2, respectively. From the context of the problem, what must be true about speeds $v_2$ and $v_3$?

3. ### Probie1

38
(1000*2.2+1100*0)=(1000*0+1100*2)

V2 and v3 have no velocity so they have no momentum...correct?

317
Correct.

5. ### Probie1

38
So because they have no momentum they cancel out which means you rewrite the equation to solve for velocity1

(1000*2.2+1100*0)=(1000*0+1100*2)

(1000)=(1100*2)

(m1)=(m2v4)

(m2V4)/m1

(1100*2)/1000

2.2ms2= 2200/1000

Is that how it is done?

6. ### Steely Dan

317
Yes, that's the idea. Conservation of momentum dictates $m_1 v_1 = m_2 v_4$, solving for the initial speed is just an algebra problem.

7. ### Probie1

38
Thanks Steely Dan... that wasn't as hard as I thought it would be... mind you that was an easy momentum problem for you, but difficult for me. I imagine it would be harder if you had 1 vehcile t-bone another and they both have pre and post impact velocities.

8. ### Probie1

38
I was just re reading your posts...

...when I re read this post the light started to flicker.

Thanks again Steely Dan

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