In: Physics
A rocket of total mass mtot = 15000 kg is initially travelling through space at 500 m/s. If it still has 11500 kg of fuel remaining, and the exhaust speed of the rocket is v(exhaust) = 3200 m/s, what is the maximum speed of the rocket?
Initial mass Mo = 15000 kg
Initial velocity vo = 500 m/s
Mass after time t is M = 11500 kg
Exhaust speed u = 3200 m/s
Speed of the rocket after time t is v = vo + u ln(Mo/M)
= 500 + 3200 ln(15000 /11500)
= 500 + 3200 ln 1.304
= 500 + 3200(0.2657)
= 500 + 850.25
= 1350.25 m/s