- #1

Dr.Brain

- 538

- 2

A rocket of mass M has "fuel and oxidizers" inside it worth 'm' kgs . When propelling the exhaust gases have a constant speed of 'v' and the GASES are emitted at a constant rate of N kg/sec .Neglecting the air resistance effects.

(a)Calculate the equation for the trajectory of the rocket taking in consideration the effect of changing "g" with altitude "y".

(b) Calculate the altitude at which rocket will burn out?

(c) Height at which no external thrust due to "g" takes place.

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For the first part, I first derived an equation for variable mass system.

F(external thrust)=M dv/dt - dM/dt (V)

where V=relative velocity of rocket and the exhaust gases

M=initial mass of rocket along with fuels

dv/dt= gradual increase in velocity of rocket as it gains altitude

I guess here external thrust will be provided by "g" since it is the only external force acting on the rocket-fuel system.

So what I did was:

F(external)=M(t) g(t) (because both mass of the rocket and value of g will be changing with altitude)

Therefore, F(external) => M(t)g(t)=M dv/dt-dM/dt ( dy/dt-v)

Beacuse "v" is the constant velocity of exhaust gases and dy/dt represent the changing velocity of the rocket .

Now I write dv/dt = differential of dy/dt

and also g(t)= g [R/y+R]^2 ( from Gravitation chapter)

And now i get a complex equation in which double integration is required .I am stuck here.Please help me if anyone here can get me a simpler metod.