Creating a solution for all the answer choices

[eri139]

Homework Statement

https://imgur.com/LYaudl1

Here is the question! Basically, we have to come up with a (reasonable) solution to all of the answer choices. It IS multiple choice, so only 1 answer is right (it is D), but we still have to find a way someone might have slipped up and made a mistake.

Homework Equations

p = mv

The Attempt at a Solution

So, I understand how to get C, D, and E. I drew a diagram and combined the vectors so the vector of the 3m mass is √2mV. And since that momentum is equal to 3mv, I solved to get v = (√2/3)V. Then for C that would just be someone making it in the opposite direction. And for E that would be solving until √2mV and leaving it as that. But I'm so lost on how someone would get 1/√3. Please help! I have been trying for 1.5 hours + and still haven't gotten anywhere.

https://imgur.com/a/mMhqV46

Here is the diagram I drew. It's basically an extension of the one in the question above.

 

[phinds]

... I drew a diagram

SAYING that you have drawn a diagram is of no help to us figuring out what the issue is. Show the diagram.

 

[eri139]

SAYING that you have drawn a diagram is of no help to us figuring out what the issue is. Show the diagram.

Okay...I didn't include it because I didn't think it was necessary since the diagram itself isn't the issue. But I'll put it in the description above.

 

[haruspex]

how someone would get 1/√3

The √2 comes from geometry, but there appears to be no way that √3 can. What equation might someone have used that would involve taking a square root to find a speed?

 

[eri139]

The √2 comes from geometry, but there appears to be no way that √3 can. What equation might someone have used that would involve taking a square root to find a speed?

Uh...forgive me if I sound really dumb, but I have no clue. I have NO idea where the root 3 could come from. I'm considering just saying it's an extra answer put in there just to trick the test-taker, since I can find no alternative.

 

[haruspex]

Uh...forgive me if I sound really dumb, but I have no clue. I have NO idea where the root 3 could come from. I'm considering just saying it's an extra answer put in there just to trick the test-taker, since I can find no alternative.

Detach your thinking from the present problem if you can. When, in solving kinetics problems, does one take a square root to find a speed?

 

[eri139]

Detach your thinking from the present problem if you can. When, in solving kinetics problems, does one take a square root to find a speed?

Would it be KE = 1/2mv^2?

Edit: okay, so now I've tried doing it like that. Would this be "correct"? :
P 1&2 = P3
P3 = 1/2m₃v^2
P1 &2 = 1/2m₃V^2
1/2mV^2 = 1/2m₃v^2
mV^2 = m₃v^2
mV^2 = 3mv^2
v = V/√3

Enough to make some physics teachers turn red with rage?

 

[haruspex]

Would it be KE = 1/2mv^2?

Edit: okay, so now I've tried doing it like that. Would this be "correct"? :
P 1&2 = P3
P3 = 1/2m₃v^2
P1 &2 = 1/2m₃V^2
1/2mV^2 = 1/2m₃v^2
mV^2 = m₃v^2
mV^2 = 3mv^2
v = V/√3

Enough to make some physics teachers turn red with rage?

That's almost what I had in mind, but need to explain why it doesn't end up as √(2/3).
Maybe take components of the velocities of the two smaller masses before calculating the KEs: ½3mv²=2(½m(V/√2)²)?

 

[eri139]

That's almost what I had in mind, but need to explain why it doesn't end up as √(2/3).
Maybe take components of the velocities of the two smaller masses before calculating the KEs: ½3mv²=2(½m(V/√2)²)?

Alright, I got it! Thank you for the help and putting up with me haha