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vodomira [7]
4 years ago
6

A rocket has initail mass M begins to move from space , with an exhaust constant speed . Find the mass of the rocket while has t

he maxmum momentum.
Physics
1 answer:
irina1246 [14]4 years ago
3 0

Answer:

m=\frac{m_{0}}{e}

Explanation:

Equation of the rocket is,

m\frac{dv}{dt} =F-v'\frac{dm}{dt}

Here, v' is the relative velocity of rocket.

In space F is zero.

So,

m\frac{dv}{dt} =-v'\frac{dm}{dt}\\dv=-v'\frac{dm}{m} \\v=-v'ln\frac{m}{m_{0} }

Now the momentum can be obtained by multiply by m on both sides.

P=-v'mln\frac{m}{m_{0} }

Now for maxima, \frac{dP}{dm}=0

-v'ln\frac{m}{m_{0} }-v'm\frac{m_{0}}{m }m_{0=0

Now,

ln(\frac{m}{m_{0} } )=-1\\\frac{m}{m_{0} }=\frac{1}{e} \\m=\frac{m_{0}}{e}

Therefore, the mass of the rocket while having maximum momentum is \frac{m_{0}}{e}

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