5_17 - t will be given by V t = V V e ln M M t-g M-M t ˙ m R where M(t is the mass of the system at time t Note that the pressure of the gas at

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Problem 5.17 Rocket accelerating against gravity After its second booster has been fired, a space vehicle finds itself outside the earth's atmosphere moving vertically upward against gravity r g at speed V 0 . Its total mass at that point is M 0 . At t = 0, the vehicle's third stage is turned on and the rocket burns propellant at a mass rate of ˙ m R kg/s. Show that if the gravitational acceleration remains essentially constant at the rocket during the firing, the rocket’s velocity V(t) after time
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Unformatted text preview: t will be given by V ( t ) = V + V e ln M M ( t ) -g [ M-M ( t )] ˙ m R where M(t) is the mass of the system at time t. Note that the pressure of the gas at the rocket exit plane, p e , will not be zero as it is in the ambient space, since the rocket exhaust is supersonic and hence the pressure at the exit is in balance with the ambient pressure. The answer given above neglects the effect of the exit plane pressure on thrust....
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.25 taught by Professor Garethmckinley during the Fall '05 term at MIT.

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