An uncovered hopper car from a freight train rolls without friction or air resistance along a level track at a constant speed of 6.70 m/s in the positive x-direction. The mass of the car is 1.18 · 105 kg.
a) As the car rolls, a monsoon rainstorm begins, and the car begins to collect water in its hopper (see the figure). What is the speed of the car after 1.62 · 104 kg of water collects in the cars hopper? Assume that the rain is falling vertically in the negative y-direction.
b) The rain stops, and a valve at the bottom of the hopper is opened to release the water. The speed of the car when the valve is opened is again 6.70 m/s in the positive x-direction (see the figure).
The water drains out vertically in the negative y-direction. What is the speed of the car after all the water has drained out?

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