# Change in Velocity after a Collision

Tags:
1. Feb 17, 2016

### x2017

1. The problem statement, all variables and given/known data
Kevin and Jake collide in the air. If Kevin undergoes a 4.2 kg*m/s change in momentum, what is Jacob’s change in velocity if he has a mass of 83.2 kg?

2. Relevant equations
p=mv
MV+mv=MV'+mv'

3. The attempt at a solution
I tried the simplest way possible...
p=mv
v=p/m
v=4.2/83.2
v=0.050m/s (incorrect)

I feel like conservation of momentum plays a role here, but I can't figure out how... I'm not great at questions where I'm given such little information...

2. Feb 17, 2016

### SammyS

Staff Emeritus
Just conservation of momentum

MV+mv=MV'+mv'

and a little algebra, rearranging.

Which variables are for Kevin? which for Jake ?

3. Feb 17, 2016

### x2017

Big letters for Kevin, small for Jake.
MV+mv=MV'+mv'
So I'm solving for:
v'=(MV+mv-MV')/m

My question now is how on Earth do I get velocities for them? Or can I just plug in the 4.2 for MV'?

Last edited: Feb 17, 2016
4. Feb 17, 2016

### SammyS

Staff Emeritus
One step at a time.

You are given Kevin's change in momentum.

How do express that with your chosen variables?

That should be related in a simple way to Jake's change in momentum..

5. Feb 17, 2016

### x2017

If Kevin's momentum changes by 4.2, then so will Jake's?

& Kevin's change in momentum could be shown as MV'-MV=4.2?

6. Feb 17, 2016

### SammyS

Staff Emeritus
So solve the conservation of momentum equation for MV'-MV .

7. Feb 17, 2016

### x2017

Alrighty,

MV'-MV=mv-mv'
4.2=mv-mv'

8. Feb 17, 2016

### SammyS

Staff Emeritus
Right.

That's actually the negative of the change in Jake's momentum.

Alternatively, that could be written as:
4.2 − (mv' − mv) =0 ,

where (mv' − mv) is the change in Jake's momentum.​

9. Feb 17, 2016

### x2017

Okay, so how would one solve for v' without v? Do we assume that v is 0?

10. Feb 17, 2016

### SammyS

Staff Emeritus
What does the question ask for?

11. Feb 17, 2016

### x2017

OOOHHHHHHH
Okay I've got it now!
change in velocity = v'-v

4.2=mv-mv'
4.2/83.2=mv-mv'
0.05=v-v'
-0.05=v'-v

I was so close at the beginning!
Thanks for your help, I'm glad I just didn't try the negative answer in the beginning, now I understand how to get there! :)

12. Feb 17, 2016

### SammyS

Staff Emeritus
Some typo / omission .
4.2/83.2 = (mv-mv')/m

Otherwise OK.

13. Feb 17, 2016

### SammyS

Staff Emeritus
The equation in post #3 wasn't too far off. It did have a major typo which it looks like you fixed..
Rearranging gives:

v' = (MV−MV' + mv)/m

= (−(MV' − MV) + mv)/m

= −(MV' − MV)/m +v​