Answer:
To find the direction and speed of the two cars after the collision, you need to perform a momentum analysis. The momentum of the two cars before the collision can be calculated as follows:
Momentum of car c = 1325 kg * 27.0 m/s = 35725 kg m/s (north)
Momentum of car d = 2165 kg * 11.0 m/s = 23815 kg m/s (east)
The total momentum of the two cars after the collision is equal to the sum of their momenta before the collision. This is a vector sum, which can be represented by an arrow pointing in the direction of the total momentum.
The final velocity of the two cars can be found by dividing the total momentum by the total mass.
Total momentum = 35725 kg m/s + 23815 kg m/s = 59540 kg m/s
Total mass = 1325 kg + 2165 kg = 3490 kg
Final velocity = Total momentum / Total mass = 59540 kg m/s / 3490 kg = 17.0 m/s
This velocity is directed somewhere between north and east. The exact direction and speed of the two cars after the collision depends on their initial positions and orientation, which are not specified in the question.