Question: 3) A mine cart weighing 1500 kg and carrying 9000 kg of finely crushed ore rolls from rest down a slope 300 m long,

3) A mine cart weighing 1500 kg and carrying 9000 kg of finely crushed ore rolls from rest down a slope 300 m long, inclined 30 below the horizontal. Unfortunately, the mine cart has a hole in the bottom, so that the ore leaks out at the rate of 300 kg/s. a) Derive the differential equation describing the motion of the mine cart. b) How much ore is left in the mine cart when it reaches bottom of the slope?

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