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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?

The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. The momentum before the collision should be equal to the momentum after the collision. Let's use the formula for momentum conservation: m1v1 (before) + m2v2 (before) = (m1 + m2)V (after), 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), V = final velocity of the combined carts (that's what you wish to find). Just put the known values into the formula and solve for V: (3.00 kg * 4.00 m/s) + (5.00 kg * 2.00 m/s) = (3.00 kg + 5.00 kg) * V 12 kg m/s + 10 kg m/s = 8.00 kg * V 22 kg m/s = 8.00 kg * V Finally, solve for V: V = 22 kg m/s / 8.00 kg = 2.75 m/s So, the speed of the two carts after they collide and stick together is 2.75 m/s.

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