Conservation of Momentum - Collisions

[doug1]

Homework Statement

A truck (4 000 kg) runs a red light and enters an intersection traveling at 81 km/h [E]. The truck collides with a car (2
000 kg) that was traveling at 54 km/h [N20oW]. Immediately after the collision the truck was traveling at 60 km/h [N
30o E]. Determine the velocity vector of the car immediately after the collision.

Homework Equations

I used the law of conservation of momentum. I used the concept that momentum is conserved in each component direction.

The Attempt at a Solution

The answer that I got was a velocity of approx 99 km/h [E32S]. Can anyone confirm this?

 

[mfb]

This would violate energy conservation, unless the truck or the car have some active system to kick away other vehicles.
I don't understand the notation for the direction, but I would expect that momentum is not conserved either.

 

[doug1]

The notation [N30E] means 30 degrees east of north for example.

Momentum is conserved in this question, but energy is not

 

[mfb]

I agree that kinetic energy does not have to be conserved, but kinetic energy cannot increase in the process.

Working in units of 1000kg*km/h:
to east:
truck initial 4*81=364
car initial -2*54*sin(20°)
truck final 4*60*sin(30°)
car final ~207 or 104 km/h
Hmm... looks wrong.

to north:
truck initial 0
car initial 2*54*cos(20°)
truck final 4*60*cos(30°)
car final -106 or -53km/h

Total energy initially: 2*81^2+1*54^2=16000 (in 1000kg*(km/h)^2)
Total energy finally: 2*60^2+1*(104^2+53^2) = 20800
Clearly this cannot happen in a car accident. The same problem appears with your result of 99km/h total speed as well.