A rocket is nothing more than a fancy tube for carrying fuel and payload—the more fuel/payload,...

A rocket is nothing more than a fancy tube for carrying fuel and payload—the more fuel/payload, the bigger the tube. Consider a rocket carrying a mass of fuel ?; the mass of the empty rocket plus payload is ? = ?? where ? < 1. The rocket burns its fuel at a rate ?, and the spent fuel is ejected out the back at a speed (relative to the rocket) ?. The rocket blasts off, aimed straight up, and continues to burn as long as it has fuel.

a. Find expressions for the net force on the rocket, its acceleration, velocity, and displacement as functions of time while the 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 is constant. Remember, F = dp/dt!

Hints:∫ ? ??=?ln(?+??)

and

∫ ln(? + ??) ?? = ? ln(? + ??) + ? ln(? + ??) − ? ?

b. Now take a real rocket, with ?=1.50×107 kg, ?=0.12, ?=9.6×104 kg/s, ? = 1200 m/s. Assuming it launches straight up from the north pole, what is the height and speed of the rocket when its fuel is used up? Is this enough to achieve escape velocity?

Expert Solution

genius_generous answered 1 year ago

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