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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?

To solve this problem, we will use the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. Momentum is calculated as mass times velocity. Before the collision: The total momentum = (mass of first cart * velocity of the first cart) + (mass of second cart * velocity of second cart) Total momentum = (3 kg * 4 m/s) + (5 kg * 2 m/s) = 12 kg*m/s + 10 kg*m/s = 22 kg*m/s After collision: The two carts stick together, so we treat them as one object with a mass of 3 kg + 5 kg = 8 kg. Let V be the velocity of the combined object (the carts) after collision. Since the total momentum before the encounter is always equal to the total momentum after the encounter due to the law of conservation of momentum, we can write the equation: 8 kg * V = 22 kg*m/s Solving for V, we get V = 22 kg*m/s / 8 kg V = 2.75 m/s So, after the inelastic collision, the speed of the two carts stuck together will be +2.75 m/s.

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