Solving 2D Momentum Collision: What is the Final Velocity After Collision?

AI Thread Summary
A collision problem involves two cars, one with a mass of 1400 kg traveling at 45 km/h and another with a mass of 1300 kg traveling at 39 km/h east. The total mass after the collision is 2700 kg. The momentum in the x and y directions was calculated, but initial calculations led to confusion regarding the application of Pythagorean theorem for resultant momentum. After clarifying the approach, the correct final velocity after the collision was determined to be approximately 30 km/h, indicating the importance of accurately summing vector components in collision problems.
aimen khattakk
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Homework Statement



One car of mass 1400 kg is traveling at 45km/h when it collides and becomes entangles with another car mass of mass 1300 kg traveling at 39km/h[E]. What is their velocity after collision

So MA = 1400 kg
VA = 45kh/h

MB = 1300 kg
VB = 39 kh/h [E]

and After Collision:
MAB = 2700kg2. Homework Equations

P = mv
∑P = ∑P'

PA + PB = PAB'

3. The Attempt at a Solution

so I've always been told to solve momentum first so since car A is going South that means it only has a verticle momentum? so
that means PAY = m⋅v
so PAY = 63000kg⋅km/h

similarly for B

so only a horizontal momentum
so PAX = 50700kg⋅km/h [E]

so now I am stuck on what to do, i tried to find the momentum of Pab in the x and y direction then find pab and solve for v but that doesn't work when i tried it. Pab in the x direction just turns out to be the same as pb in the x direction and pab in y direction turns out to be pa in y direction and then using pythaguras theorum to find the hyp and hence find Pab i get 37396 kg⋅km/h and then solving for V by diving the Pab by the total mass of both of the cars together gives me a velocity of 13.85km/h but the answer is 30.0km/h so i think i messed up after solving my momentums for before the collision but idk what i did wrong
 
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Check your Pythagoras calculation again. Show your working.
 
aimen khattakk said:
then using pythaguras theorum to find the hyp and hence find Pab i get 37396 kg⋅km/h
This number is not correct.

Edit: NascentOxygen beat me to it.
 
okay so
PABY' = 63000kg⋅km/h and PABX = 50700 kg⋅km/h [E]

so

c2 = a2 + b2
so
c2 = 630002 + 507002
c2 = √630002 + 507002
so c = 37396.6576 kg⋅km/h so this is PAB '

now i need to find the velocity after collison so i took the combined mass and divided it with 37396.6576kg⋅km/h
and my v ends up being 13.85 km/h but the answer is 30 km SE
 
i do not understand hot i
DrClaude said:
This number is not correct.

Edit: NascentOxygen beat me to it.
it is? i don't understand how because i did
507002 + 630002
and since 63000 is actually in the negative direction i basically did

507002 - 630002
and then square rooted it. do i not assign that negative direction? but its going south?
 
The negative sign isn't applicable here. You use Pythagoras to calculate magnitude.
 
aimen khattakk said:
i don't understand how because i did
507002 + 630002
and since 63000 is actually in the negative direction i basically did

507002 - 630002
and then square rooted it. do i not assign that negative direction? but its going south?
What if A was going North instead? Do you expect a different result? Making a diagram of the situation would help.
 
my calculator is fine, I've used it for all my courses and I am in 2 other math courses so its not broken, but i took ur advice and tried it with another one and still getting the same answer
 
DrClaude said:
What if A was going North instead? Do you expect a different result? Making a diagram of the situation would help.
oh wait, so since I am looking for the overall momentum of Pab after the collision, i don't need to consider negative and positives? since I am not going in a specific direction, rather I am going in 2 directions not one?
 
  • #10
aimen khattakk said:
my calculator is fine, I've used it for all my courses and I am in 2 other math courses so its not broken, but i took ur advice and tried it with another one and still getting the same answer
NascentOxygen said that because
aimen khattakk said:
c2 = 630002 + 507002
c2 = √630002 + 507002
so c = 37396.6576
is not correct. But this is not what you calculated, as you stated in a subsequent post.
 
  • #11
DrClaude said:
What if A was going North instead? Do you expect a different result? Making a diagram of the situation would help.
and I am basically looking for the sum of 2 vectors so it would be that the cars are going S of E not just S or just E so doing what i did earlier would have made the direction be just south right?
 
  • #12
aimen khattakk said:
oh wait, so since I am looking for the overall momentum of Pab after the collision, i don't need to consider negative and positives? since I am not going in a specific direction, rather I am going in 2 directions not one?

aimen khattakk said:
and I am basically looking for the sum of 2 vectors so it would be that the cars are going S of E not just S or just E so doing what i did earlier would have made the direction be just south right?
You already have the sum of the two vectors. What you are looking for is the magnitude of the resultant vector.
 
  • #13
DrClaude said:
NascentOxygen said that because

is not correct. But this is not what you calculated, as you stated in a subsequent post.
that is the Pab not the velc
DrClaude said:
You already have the sum of the two vectors. What you are looking for is the magnitude of the resultant vector.

OH so since I am looking for the magnitude i don't need to consider their directions so it would just be

c2 = 630002+ 507002
c2 = √630002 + 507002
so c = 80867.11 kg⋅km/h ??

so then velocity would be 80867.11 kg⋅km/h / 2700kg
so v = 29.9 km/h! thank you! that makes so much more sense!
 
  • #14
You are adding two perpendicular quantities. The hypotenuse will be longer than either of the perpendicular components.
 
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