(hrw8c9p40) A space vehicle is traveling at 4350 km/h relative to the Earth when the exhausted rocket motor is disengaged and sent backward

Question

(hrw8c9p40) A space vehicle is traveling at 4350 km/h relative to the Earth when the exhausted rocket motor is disengaged and sent backward with a speed of 64 km/h relative to the command module. The mass of the motor is four times the mass of the module. What is the speed (km/h) of the command module relative to Earth after the separation?

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Adela 2 months 2021-07-30T03:46:13+00:00 1 Answers 2 views 0

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    2021-07-30T03:47:20+00:00

    Answer:4298.8 km/h

    Explanation:

    Given

    velocity of space vehicle v_i=4350\ km/h

    Mass of motor is 4 times the mass of module

    suppose m is the mass of module therefore

    mass of motor is 4 m

    velocity of disengaged motor is 64 km/h   relative to command module

    we can write

    v_{me}=v_{mc}+v_{ce}

    where v_{me}=velocity of motor relative to earth

    v_{mc}=velocity of motor relative to command module

    v_{ce}=velocity of command relative to earth

    Conserving momentum

    M(v_i)=4m(v_{me})+mv_{ce}

    where M is combined mass of motor and module

    Mv_i=4m(v_{mc}+v_{ce})+mv_{ce}

    5mv_i=4mv_{mc}+4mv_{ce}+mv_{ce}

    5mv_i=4mv_{mc}+5mv_{ce}

    v_{ce}=v_i-\frac{4}{5}\times v_{mc}

    v_{ce}=4350-\frac{4}{5}\times 64

    v_{ce}=4350-51.2

    v_{ce}=4298.8\ km/h

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