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  • A rocket of mass 1000 Kg set for vertical firing the exhaust speed is 200 m/s to give on initial acceleration of <img alt="15 m/s^2" src="http://entrancecorner.oncodecogs.com/gif.latex?15%20m/

A rocket of mass 1000 Kg set for vertical firing the exhaust speed is 200 m/s to give on initial acceleration of 15 m/s^2  what will be the amount of gas ejected per second (in Kg/s ) to supply the needed thrust (g = 10 m/s )

Option: 1

125


Option: 2

100


Option: 3

150


Option: 4

75


Answers (1)

best_answer

As we have learned

Acceleration of Rocket -

a=\frac{u}{m}\:\frac{dm}{dt}-g

 

\:a=\frac{u }{m}\: \frac{dm}{dt}\:[\text{If\:g\:is neglected}]

- wherein

Instantaneous Velocity of Rocket

v=u\:log_{e}\left ( \frac{m_{\circ }}{m} \right )-gt

m_{\circ }\rightarrow Initial\:mass\:of\:Rocket

 Force applied by the gases on the rocket = \frac{v dm }{dt }

\frac{v dm }{dt }- mg = ma

\frac{dm }{dt } = \frac{m(g+a)}{v} = \frac{1000(10+15)}{200} = 125 Kg /s

 

Posted by

Gautam harsolia

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