A rocket of total mass mtot = 15000 kg is initially travelling through space at 500...

A rocket of total mass m_tot = 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?

Expert Solution

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

genius_generous answered 6 months ago

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