Final answer:
The velocity with which the truck and car move together after the collision is -16.625 m/s to the west.
Step-by-step explanation:
To find the velocity with which the two vehicles move together after the collision, we need to use the principles of conservation of momentum. The initial momentum of the truck is given by its mass (2.00 × 10^3 kg) multiplied by its velocity (-14.0 m/s, since it is moving west), while the initial momentum of the car is given by its mass (1.20 × 10^3 kg) multiplied by its velocity (-21.0 m/s, since it is moving south).
Using the principle of conservation of momentum, the total initial momentum of the system (truck + car) is equal to the total final momentum of the system after the collision. Since the vehicles move together after the collision, their final velocity must be the same. Therefore, we can set up the following equation to solve for the final velocity:
(2.00 × 10^3 kg × -14.0 m/s) + (1.20 × 10^3 kg × -21.0 m/s) = (2.00 × 10^3 kg + 1.20 × 10^3 kg) × v
Simplifying the equation, we find:
-28.00 × 10^3 kg·m/s - 25.20 × 10^3 kg·m/s = 3.20 × 10^3 kg × v
-53.20 × 10^3 kg·m/s = 3.20 × 10^3 kg × v
Dividing both sides of the equation by 3.20 × 10^3 kg, we get:
v = -53.20 × 10^3 kg·m/s / 3.20 × 10^3 kg
v = -16.625 m/s
Therefore, the velocity with which the truck and car move together after the collision is -16.625 m/s (to the west).