The final velocity of the cars after the collision is approximately -10.78 m/s due south.
To calculate the final velocity of the cars after the collision, we can use the principle of conservation of momentum.
1. The momentum of an object is the product of its mass and velocity. The total momentum before the collision is equal to the total momentum after the collision.
2. Let's assign positive directions to the east and north and negative directions to the west and south.
3. The momentum of the first car before the collision is given by the product of its mass and velocity: 1200 kg * (-8.00 m/s) = -9600 kg·m/s. The negative sign indicates that the momentum is directed south.
4. The momentum of the second car before the collision is: 850 kg * (-17.0 m/s) = -14450 kg·m/s. The negative sign indicates that the momentum is directed west.
5. To find the total momentum before the collision, we need to add the momenta of the two cars: -9600 kg·m/s + (-14450 kg·m/s) = -24050 kg·m/s.
6. Since the cars stick together after the collision, their final velocity will be the same. Let's represent the final velocity of the cars by V.
7. The total momentum after the collision is equal to the product of the total mass (sum of the masses of the two cars) and the final velocity: (1200 kg + 850 kg) * V.
8. According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision: -24050 kg·m/s = (1200 kg + 850 kg) * V.
9. Solving this equation, we find the final velocity of the cars after the collision: V = -24050 kg·m/s / (1200 kg + 850 kg).
10. Plugging in the values, we get V ≈ -10.78 m/s.
11. The negative sign indicates that the final velocity is directed south, which means the cars will continue moving in the same direction as the first car's initial velocity.