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

[aimen khattakk]

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 M_A = 1400 kg
V_A = 45kh/h

M_B = 1300 kg
V_B = 39 kh/h [E]

and After Collision:
M_AB = 2700kg2. Homework Equations

P = mv
∑P = ∑P'

P_A + P_B = P_AB'

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 P_AY = m⋅v
so P_AY = 63000kg⋅km/h

similarly for B

so only a horizontal momentum
so P_AX = 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

 

[NascentOxygen]

Check your Pythagoras calculation again. Show your working.

 

[DrClaude]

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.

 

[aimen khattakk]

okay so
P_ABY' = 63000kg⋅km/h and P_ABX = 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 P_AB '

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

 

[aimen khattakk]

i do not understand hot i

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?

 

[NascentOxygen]

The negative sign isn't applicable here. You use Pythagoras to calculate magnitude.

 

[DrClaude]

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.

 

[aimen khattakk]

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

 

[aimen khattakk]

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?

 

[DrClaude]

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

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.

 

[aimen khattakk]

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?

 

[DrClaude]

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?

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.

 

[aimen khattakk]

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

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!

 

[NascentOxygen]

You are adding two perpendicular quantities. The hypotenuse will be longer than either of the perpendicular components.