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A rocket has total mass M, = 360 kg, including M, 330 kg of fuel and oxidizer. In interstellar space, it starts from rest at the position x = 0, turns on its engine at time t = 0, and puts out exhaust with rel- ative speed v, = 1 500 m/s at the constant rate k = 2.50 kg/s. The fuel will last for a burn time of T, = Mfuet/ k = 330 kg/(2.5 kg/s) = 132 s. (a) Show that during the burn the velocity of the rocket as a function of time is given by fuel kt v(i) = - v, In( 1 M, (b) Make a graph of the velocity of the rocket as a function of time for times running from 0 to 132 s. (c) Show that the acceleration of the rocket is kv, a(1) M: - kt (d) Graph the acceleration as a function of time. (e) Show that the position of the rocket is M, 'n = (1)x t In (1 k + vt (f) Graph the position during the burn as a function of time.

A rocket has total mass M, = 360 kg, including M, 330 kg of fuel and oxidizer. In interstellar space, it starts from rest at the position x = 0, turns on its engine at time t = 0, and puts out exhaust with rel- ative speed v, = 1 500 m/s at the constant rate k = 2.50 kg/s. The fuel will last for a burn time of T, = Mfuet/ k = 330 kg/(2.5 kg/s) = 132 s. (a) Show that during the burn the velocity of the rocket as a function of time is given by fuel kt v(i) = - v, In( 1 M, (b) Make a graph of the velocity of the rocket as a function of time for times running from 0 to 132 s. (c) Show that the acceleration of the rocket is kv, a(1) M: - kt (d) Graph the acceleration as a function of time. (e) Show that the position of the rocket is M, 'n = (1)x t In (1 k + vt (f) Graph the position during the burn as a function of time.

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A rocket has total mass M, = 360 kg, including M, 330 kg of fuel and oxidizer. In interstellar space, it starts from rest at the position x = 0, turns on its engine at time t = 0, and puts out exhaust with rel- ative speed v, = 1 500 m/s at the constant rate k = 2.50 kg/s. The fuel will last for a burn time of T, = Mfuet/ k = 330 kg/(2.5 kg/s) = 132 s. (a) Show that during the burn the velocity of the rocket as a function of time is given by fuel kt v(i) = - v, In( 1 M, (b) Make a graph of the velocity of the rocket as a function of time for times running from 0 to 132 s. (c) Show that the acceleration of the rocket is kv, a(1) M: - kt (d) Graph the acceleration as a function of time. (e) Show that the position of the rocket is M, 'n = (1)x t In (1 k + vt (f) Graph the position during the burn as a function of time.
Transcribed Image Text:A rocket has total mass M, = 360 kg, including M, 330 kg of fuel and oxidizer. In interstellar space, it starts from rest at the position x = 0, turns on its engine at time t = 0, and puts out exhaust with rel- ative speed v, = 1 500 m/s at the constant rate k = 2.50 kg/s. The fuel will last for a burn time of T, = Mfuet/ k = 330 kg/(2.5 kg/s) = 132 s. (a) Show that during the burn the velocity of the rocket as a function of time is given by fuel kt v(i) = - v, In( 1 M, (b) Make a graph of the velocity of the rocket as a function of time for times running from 0 to 132 s. (c) Show that the acceleration of the rocket is kv, a(1) M: - kt (d) Graph the acceleration as a function of time. (e) Show that the position of the rocket is M, 'n = (1)x t In (1 k + vt (f) Graph the position during the burn as a function of time.
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