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A rocket is fired in deep space, where gravity is negligible. In the first second it ejects 1/160 of its mass as exhaust gas and has an acceleration of 15.1 m/s^2.What is the speed v_gas of the exhaust gas relative to the rocket?

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    A rocket is fired in deep space, where gravity is negligible. In the first second it ejects 1/160 of its mass as exhaust gas and has an acceleration of 15.1 m/s^2.What is the speed v_gas of the exhaust gas relative to the rocket?

    By means of the rocket equation,

    deltaV = cln(Wo/Wt) where
    deltaV or dV = the incremental change in velocity over a given time period, Wo = the initial weight at ignition, Wt = the weight after a specific time period and c = the velocity of the exhaust gases. ln = the natural logarithm of.

    After one second of firing, the rocket achieves a speed of 15.m/s.

    Therefore,
    dV = 15.1 = cln[Wo/(Wo-Wo/160)
    ...= ]5.1 = cln[1/(1-1/160] = ............cln(1.006289)

    15.1 = cln(1.006289) - c(.0062696


    Hence, c = 2408m/s

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