## Rocket- Work Integration

Limits, differentiation, related rates, integration, trig integrals, etc.
paulh428
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### Rocket- Work Integration

Hello, I have a problem I'm working on and having some problems on how to go about it. Here's the problem:
A rocket weighing 3 tons is filled with 40 tons of liquid fuel. In the initial part of the flight, fuel is burned off at a constant rate of 2 tons per 1000 ft of vertical height. How much work is done in lifting the rocket to 3000 ft?
So far, all I have is the force is 43 tons(?- not sure if this is right). And the limits of integration from 0 to 3000. That is all I have. Any help would be appreciated.

If you need the answer to verify: 120,000 ft-tons.

nona.m.nona
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### Re: Rocket- Work Integration

paulh428 wrote:A rocket weighing 3 tons is filled with 40 tons of liquid fuel. In the initial part of the flight, fuel is burned off at a constant rate of 2 tons per 1000 ft of vertical height. How much work is done in lifting the rocket to 3000 ft?

Since the work is in terms of thousands of feet, it might be helpful to use limits of x = 0 to x = 3, where "x" is defined in terms of "thousands of feet".

Use algebra to create an expression for the tonnage, in terms of x. Your starting value is correct: 43. The rate of change (that is, the slope) is -3, with the change being with respect to x. What integrand does this create?

Martingale
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### Re: Rocket- Work Integration

I get

$\int\limits_{0}^{3000}\left[3+\left(40-\frac{2}{1000}x\right)\right]dx$