A rocket is nothing more than a fancy tube for carrying fuel andpayload—the more fuel/payload, the bigger the tube. Consider arocket carrying a mass of fuel ?; the mass of the empty rocket pluspayload is ? = ?? where ? < 1. The rocket burns its fuel at arate ?, and the spent fuel is ejected out the back at a speed(relative to the rocket) ?. The rocket blasts off, aimed straightup, and continues to burn as long as it has fuel.
a. Find expressions for the net force on the rocket, itsacceleration, velocity, and displacement as functions of time whilethe rocket is still burning. You may assume gravity is constant(i.e. the displacement is much less than the radius of
the Earth) but you may not assume the mass of the rocket isconstant. Remember, F = dp/dt!
Hints:∫ ? ??=?ln(?+??)
and
∫ ln(? + ??) ?? = ? ln(? + ??) + ? ln(? + ??) − ? ?
b. Now take a real rocket, with ?=1.50×107 kg, ?=0.12, ?=9.6×104kg/s, ? = 1200 m/s. Assuming it launches straight up from the northpole, what is the height and speed of the rocket when its fuel isused up? Is this enough to achieve escape velocity?
