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A rocket that is in deep space and initially at rest relative to an inertial reference...

A rocket that is in deep space and initially at rest relative to an inertial reference frame has a mass of 2.80 105 kg, of which 1.92 105 kg is fuel. The rocket engine is then fired for 250 s while fuel is consumed at the rate of 480 kg/s. The speed of the exhaust product relative to the rocket is 3.21 km/s.
(a) What is the rocket's thrust?
N

(b) What is the mass of the rocket after the 250 s firing?
kg

(c) What is the speed of the rocket after the 250 s firing?
m/s

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Answer #1

a)

thrust = ve * (dM/dt) = 3.21*1000/480 = 6.688 N

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b)
m = (dM/dt) * t = 480 * 250 = 120000 kg = 1.2 * 10^5 Kg

M' = M - m = 2.80*10^5 - 1.2*10^5 = 1.6*10^5 Kg

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c)

v = ve * ln(Mi/Mf)

   = 3.21*1000 * ln(2.80*10^5/1.6*10^5)

   = 1796.37 m/s

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