A rocket is intended to leave the earth's gravitational field. The fuel in its main engine is little less than the amount that is necessary, and an auxillary engine, only capable of operating for a short time, has to be used as well.

When is it best to fire the auxillary engine: at take-off, or when the the rocket has nearly stopped w.r.t earth, or does it not matter?

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## Comments

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TopNewestUmm According to me, it doesn't matter. See, anything escapes the Earth's Gravitational Field, when it attains the escape velocity, which is almots 11.2Km/s. Now, this velocity is calculated for a body thrown from the surface of Earth, i.e. if you throw a body from the SURFACE of Earth, with this velocity, it would escape the field. So, if the amount of fuel is less, then that means that the rocket won't be able to hit the escape speed and would either remain in orbit or crash down. So, to prevent that the Auxillary engine could be used at the takeoff.

On the other hand, let's assume that the rocket is just about to come to rest. At this instant, it would have some potential energy, and a little amount of Kinetic Energy, which won't be enough to escape the field. Firing the Auxillary engine at this instant, would increase the velocity, hence increasing the Total energy of the rocket, as a result helping it to escape the field.

Please correct me if I'm wrong:)

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Hint: When is \( F \neq ma \)?

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if you are in space, then Einstein theory comes in...

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Wrong answer: it matters. I too had thought the same

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Can you elaborate??

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I assume that the fuel has a constant calorific value which is to say that no matter where it is combusted , it will produce the same amount of energy, and now taking into account that earth has a viscous atmosphere (relative to space) , it should use auxillary engine when it is close to infinity to minimise loss due to attentuation (frictional losses)

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Ignore all dissipative forces

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It doesnot matter since every planet have its own gravitational field, if rocket just left the earths gravitational field then it will be automatically attracted towards intended planet since no external force is going to act and only force is going to be the gravitational force of the intended planet therefore no fuel is going to be used up. BY THE WAY ROCKET IS EQUIPPED WITH SOLAR PANELS WHICH MEANS THAT IT IS GOING TO CHARGE ITSELF AND WILL NO LONGER DEPEND ON FUEL

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@Ronak Agarwal , @Deepanshu Gupta @Mvs Saketh @jatin yadav @josh silverman @Calvin Lin @David Mattingly , try this challenge, it's awesome.....

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I think when the rocket has nearly stopped.

Use the main engine first, it will decrease the rocket's mass (because it loss fuel). After that u can use the auxiliary engine. Neglecting other aspect, we have Resultant of Impulse = momentum. With the new mass of rocket which is far fewer, it will produce higher velocity so that the rocket can leave the earth's gravitational field.

CMIIW :D

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