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Question: A 3.00-kg cart with an initial velocity of +4.00 collides inelastically with a 5.00-kg cart with an initial velocity of +2.00 The carts stick together when they collide. What is their speed after colliding?

This is a problem involving conservation of momentum where the objects in the system stick together, making it an inelastic collision. In an inelastic collision, the momentum before the collision should equal the momentum after the collision. This can be expressed using the formula: m1*v1 + m2*v2 = (m1 + m2)*Vf where m1 = mass of the first cart = 3.00 kg v1 = initial velocity of the first cart = +4.00 m/s m2 = mass of the second cart = 5.00 kg v2 = initial velocity of the second cart = +2.00 m/s Vf = final velocity of the combined carts We need to find Vf, the final velocity of the two carts combined. Rearranging the equation above and substituting the known values you will get: Vf = (m1*v1 + m2*v2) / (m1 + m2) = (3.00 kg * 4.00 m/s + 5.00 kg * 2.00 m/s) / (3.00 kg + 5.00 kg) = (12 kg*m/s + 10 kg*m/s) / 8.00 kg = 22 kg*m/s / 8.00 kg = 2.75 m/s Therefore, the speed of the combined carts after they collide is 2.75 m/s.

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