How Is the Total Momentum Calculated in a Two-Car Collision?

[mybrohshi5]

Homework Statement

Two identical cars (m = 1350 kg) are traveling at the same speed (25 m/s). Car A is going 30 degrees East of North and car B is going 60 degrees West of North. What is the magnitude of the total momentum of the two-car system.

Homework Equations

p = mv

The Attempt at a Solution

I found the x and y components of the momentum of each car. Then i added the similar components together. So then to find the momentum of the system i took the sqrt of the x and y components squared and added together.

x component car A
1350kg(25m/s)(cos60) = 16875

x component of car B
1350kg(25m/s)(cos30) = 29228

Total x component momentum = 46103y component of car A
1350kg(25m/s)(sin60) = 29228

y component of car B
1350kg(25m/s)(sin30) = 16875

Total y component momentum = 46103so the total momentum of the system is

P_total = sqrt ((46103^2) + (46102^2))

P_total = 65199 kgm/s

This is wrong though.

The correct answer is 47700 kgm/s

Can anyone help me get the right answer.

Thank you :)

 

[rl.bhat]

x components of momentum are in the opposite direction.
So
total x component momentum = ...?

 

[mybrohshi5]

x component of car B is actually

-29228 so the total x component is -12353

so the total momentum of the system is

P_total = sqrt ((46103^2) + (-12353^2))

P_total = 47730kgm/s

:)

Thank you