What is the momentum after the collision
What is the momentum of the red cart after the collision
What is the velocity of the red cart after collision

The momentum after the collision is .

The momentum of the red cart after the collision is

The velocity of the red cart after the collision is  .

Explanation:

The law of conservation of momentum says that momentum before the collision must equal the momentum after the collision; therefore, the momentum after the collision equals (which is the momentum before the collision).

After the collision, the conservation of momentum demands that

which is the velocity of the red cart after the collision.

Finally, the momentum of the red cart is after the collision is

Thus, the total momentum after the collision is  , and of the red cart is , and the velocity of the red cart after the collision is  .

the body's situation won't change the forces are equal opposit and on the same body

not too sure thinking all accelerations are pointed down