A rocket has a mass of 1*10^6 kg including fuel. Determine the constant rate at

Question

A rocket has a mass of 1*10^6 kg including fuel. Determine the constant rate at which the fuel must be burned so that its thrust gives the rocket a speed of 100 m/s in 10 seconds starting from rest with a vertical trajectory. The fuel exhausts from the rocket at a relative speed of 1000 m/s. Neglect air resistance and assume gravity is constant.

We want to find the change in mass (m), and the Force of the thrust. The change in mass equals 17971.22 and the Force of the thrust equals 17.97.

I need to know the process.

Explanation / Answer

for vertical rocket,we have following equation

Vfinal=Vintial+Vexhaust*ln(Mi/Mf)-gt

100=0+1000 * ln(10^6/Mf ) - 9.8*10

solving,,,,,,,

cange in mass=Mf - Mi=179630.14kg

again,

thrust= Ve (dm/dt)=1000*(179630/10)=17.96 MN

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