Answer:
A
Step-by-step explanation:
The final velocity of the truck can be calculated using the law of conservation of momentum. The law states that the total momentum of a closed system (the car and truck) remains constant unless an external force acts on the system.
Let's call the final velocity of the system (car + truck) after the collision vf.
The initial momentum of the car before the collision is equal to m1 * v1 = 1500 kg * 20 m/s = 30000 kg m/s, where m1 is the mass of the car and v1 is its initial velocity.
The initial momentum of the truck before the collision is equal to m2 * v2 = 2500 kg * -30 m/s = -75000 kg m/s, where m2 is the mass of the truck and v2 is its initial velocity.
The total initial momentum of the system before the collision is equal to the sum of the initial momenta of the car and truck:
p_initial = m1 * v1 + m2 * v2 = 30000 kg m/s + (-75000 kg m/s) = -45000 kg m/s.
After the collision, the final momentum of the system is equal to the sum of the final momenta of the car and truck:
p_final = m1 * vf + m2 * vf = (1500 kg + 2500 kg) * vf = 4000 kg * vf.
Since the total momentum of the system is conserved, we can set the initial and final momenta equal to each other:
-45000 kg m/s = 4000 kg * vf
Finally, we can solve for the final velocity of the system (truck):
vf = -45000 kg m/s / 4000 kg = -11.25 m/s
Since the truck was moving west before the collision, the final velocity is 11.25 m/s west, so the answer is A. 11.25 m/s west.