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16 September, 10:01

A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 50.2 * 105 kg, of which 12.5 * 105 kg is fuel. The rocket engine is then fired for 450 s, during which fuel is consumed at the rate of 370 kg/s. The speed of the exhaust products relative to the rocket is 4.90 km/s. (a) What is the rocket's thrust? After the 450 s firing, what are (b) the mass and (c) the speed of the rocket?

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  1. 16 September, 11:45
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    165.2762 m/sec

    Explanation:

    The initial mass of the rocket and the fuel

    M₀ = 5.02e6 kg

    The initial mass of the fuel

    Mf₀ = 1.25e6 kg

    The rate of fuel consumption

    dm/dt = 370 kg/sec

    The duration of the rocket burn

    Δt = 450 sec

    The rocket exhaust speed

    Ve = 4900 m/sec

    The thrust, T

    T = Ve (dm/dt) = 1813000 kg m/sec²

    The mass of the expended propellant, ΔM

    ΔM = Δt (dm/dt) = 166500 kg

    The rocket's mass after the burn

    M₁ = M₀ - ΔM = 4853500 kg

    The speed of the rocket after the burn

    Δv = Ve ln (M₀/M₁) = 165.2762 m/sec
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