Final answer:
The center-of-mass velocity of two colliding cars that stick together after the collision will not change because momentum is conserved. This is evident when calculating the combined momentum before the collision and knowing that they move as one unit without external horizontal forces after the collision.
Step-by-step explanation:
In the scenario where Car A has a mass of 2000 kg and approaches an intersection with a velocity of 38 m/s directed to the east, and Car B has a mass of 3500 kg and approaches the intersection with a velocity of 53 m/s directed 63° north of east, the two cars collide and stick together. The center-of-mass velocity will not change as a result of the collision because momentum is conserved in the absence of external forces.
To calculate the center-of-mass velocity before the collision:
- Resolve the velocity of Car B into x and y components.
- Calculate the momentum of both cars in the x and y directions.
- Divide the total momentum by the total mass of the system to get the velocity components of the center of mass.
After the collision, the velocity of the center of mass will be the same since the cars stick together and move as one object, and there are no external forces involved in the horizontal plane.