An railroad car with an open top is rolling along a straight, level track with speed '00. There is no engine, it's just the car rolling along. Assume there is no friction or air drag, the net force on the car is zero, so it is moving with constant velocity. A sudden rainstorm comes along and water starts lling the car. From conservation of momentum, the speed of the car will have to decrease as its mass increases. a. Show that conservation of momentum leads to me = (m + dm)(v + dv) where m and v are the initial mass and speed of the car, dm is the mass of water that enters the car in time dt and dc is the resulting change in velocity. b. Show that the equation from a) reduce to m dc = dm n which is a separable differential equation and solve for v as a function of m Hint: assume the term dm (it) is small enough to be ignored. c if the initial mass of the car is 10000 kg and initial velocity is 10 m/s, what is the velocity when the mass has doubled to 20000 kg