A rocket travels through the atmosphere and experiences a linear drag force given by -ku, where k is a positive constant. Assume that all other external forces are negligible (e.g. ignore gravity). Let m; be the initial mass of the rocket plus fuel and m, is the final mass of the rocket after all the fuel has burned, and u is the speed of the exhaust fuel relative to the rocket. a) Write down the differential equation of motion (i.e. Newton's 2nd Law). b) The rocket burns fuel at a constant rate a = -dm/dt. Assuming that the rocket begins from rest, what is the final speed of the rocket in terms of m,, my, a, u, and k.

A rocket travels through the atmosphere and experiences a linear drag force given by -ku, where k is a positive constant. Assume that all other external forces are negligible (e.g. ignore gravity). Let m; be the initial mass of the rocket plus fuel and m, is the final mass of the rocket after all the fuel has burned, and u is the speed of the exhaust fuel relative to the rocket. a) Write down the differential equation of motion (i.e. Newton's 2nd Law). b) The rocket burns fuel at a constant rate a = -dm/dt. Assuming that the rocket begins from rest, what is the final speed of the rocket in terms of m,, my, a, u, and k.