Solve 2D Momentum Problem: Car1 Velocity at Impact

[Probie1]

Homework Statement

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?

Homework Equations

(m1v1+m2v2)=(m1v3+m2v4)

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 ?

 

[Steely Dan]

Homework Statement

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?

Homework Equations

(m1v1+m2v2)=(m1v3+m2v4)

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 ?

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 $v_3$?

 

[Probie1]

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

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

 

[Steely Dan]

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

Correct.

 

[Probie1]

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?

 

[Steely Dan]

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.

 

[Probie1]

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.

 

[Probie1]

I was just re reading your posts...

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.

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

Thanks again Steely Dan