On an absolutely smooth surface, a box of sand with a mass of 9 kg moves at a speed of 6 m / s.

On an absolutely smooth surface, a box of sand with a mass of 9 kg moves at a speed of 6 m / s. A weight weighing 1 kg falls into the sand, release without initial speed from ten meters height. Determine the speed of the box after the weight hits it.

Let’s use the law of conservation of momentum. Since the surfaces are perfectly smooth, there is no friction force, which means that the system can be considered closed. The impulse in the closed system remains constant. The impulse before the weight falls is determined by the product mt of the mass of the box with 9 kg of sand by the trolley speed Vt 6 m / s. The impulse after the fall will be determined by the product mt of the mass of the box with sand and mg of the mass of a 1 kg weight by the speed of their movement V. mt * Vt = (mt + mg) * V; V = mt * Vt / (mt + mg); V = 9kg * 6m / s / (9kg + 1kg) = 5.4m / s.
Answer: V = 5.4 m / s.