Change in Velocity after a Collision

[x2017]

Homework Statement

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?

Homework Equations

p=mv
MV+mv=MV'+mv'

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...

 

[SammyS]

Homework Statement

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?

Homework Equations

p=mv
MV+mv=MV'+mv'

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...

Just conservation of momentum

MV+mv=MV'+mv'

and a little algebra, rearranging.

Which variables are for Kevin? which for Jake ?

 

[x2017]

Just conservation of momentum

MV+mv=MV'+mv'

and a little algebra, rearranging.

Which variables are for Kevin? which for Jake ?

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'?

 

[SammyS]

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'?

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..

 

[x2017]

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..

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?

 

[SammyS]

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?

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

 

[x2017]

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

Alrighty,

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

 

[SammyS]

Alrighty,

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

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.​

 

[x2017]

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.​

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

 

[SammyS]

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

What does the question ask for?

what is Jacob’s change in velocity

 

[x2017]

What does the question ask for?

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! :)

 

[SammyS]

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! :)

Some typo / omission .

4.2/83.2 = (mv-mv')/m​

Otherwise OK.

 

[SammyS]

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

v'=(MV+mv-MV')/m
...

Rearranging gives:

v' = (MV−MV' + mv)/m

= (−(MV' − MV) + mv)/m

= −(MV' − MV)/m +v​