A rocket, fired from rest at time t = 0, has an initial mass of m0 (including its fuel). Assuming that the fuel is consumed at a constant rate k, the mass m of the rocket, while fuel is being burned, will be given by m0 – kt. It can be shown that if air resistance is neglected and the fuel gases are expelled at a constant speed c relative to the rocket, then the velocity v of the rocket will satisfy the equation dv m. dt ck mg where g is the acceleration due to gravity. (a) Find v(t) keeping in mind that the mass m is a function of t. m/sec v(t) =

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