A 12000 kg truck strikes the back end of a 750 kg car moving at 15 m/s. If the truck loses 7500 kg-m/s of its momentum to the car, what is the car's velocity after the collision?

I'm not sure how to solve this one... Help please?!

To solve this problem, we need to apply the principle of conservation of linear momentum. The total momentum before the collision should be equal to the total momentum after the collision.

Let's calculate the initial momentum of both the truck and the car separately before the collision:

Initial momentum of the truck = mass of the truck x velocity of the truck
Initial momentum of the truck = 12000 kg x 0 m/s (assuming the truck is initially at rest)

Initial momentum of the car = mass of the car x velocity of the car
Initial momentum of the car = 750 kg x 15 m/s

Now, let's calculate the final momentum of both the truck and the car after the collision:

Final momentum of the truck = (mass of the truck - momentum transferred) x velocity of the truck
Final momentum of the car = (mass of the car + momentum transferred) x velocity of the car

Given that the truck loses 7500 kg-m/s of its momentum to the car, we can calculate the final momentum of the truck:

Final momentum of the truck = (12000 kg - 7500 kg-m/s) x velocity of the truck

Now, using the conservation of linear momentum, we know that the total momentum before the collision equals the total momentum after the collision:

Initial momentum of the truck + initial momentum of the car = Final momentum of the truck + Final momentum of the car

12000 kg x 0 m/s + 750 kg x 15 m/s = (12000 kg - 7500 kg-m/s) x velocity of the truck + (750 kg + 7500 kg-m/s) x velocity of the car

Now we can solve this equation to find the velocity of the car after the collision.