“At time t = 0 a 2330-kg rocket in outer space fires an engine that exerts” an increasing force on it in the +x-direction. This force obeys

Question

“At time t = 0 a 2330-kg rocket in outer space fires an engine that exerts” an increasing force on it in the +x-direction. This force obeys the equation Fx=At2, where t is time, and has a magnitude of 781.25 N when t = 1.27 s .

What impulse does the engine exert on the rocket during the 1.50- s interval starting 2.00 s after the engine is fired?

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Khánh Gia 3 years 2021-08-24T04:32:29+00:00 1 Answers 251 views 0

Answers ( )

  1. thienhuong
    0
    2021-08-24T04:33:37+00:00
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    Answer:

    Imp = 5626.488\,\frac{kg\cdot m}{s}

    Explanation:

    First, it is required to model the function that models the increasing force in the +x direction:

    a =\frac{781..25\,N}{(1.27\,s)^{2}}

    a = 484 \frac{N}{s^{2}}

    The equation is:

    F_{x} = 484\,\frac{N}{s^{2}}\cdot t^{2}

    The impulse done by the engine is given by the following integral:

    Imp=484\,\frac{N}{s^{2}} \int\limits^{3.50\,s}_{2\,s} {t^{2}} \, dt

    Imp = 161.333\,\frac{N}{s^{2}}\cdot [(3.50\,s)^{3}-(2\,s)^{3}]

    Imp = 5626.488\,\frac{kg\cdot m}{s}

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