a 2140 kg rocket has 4090 kg of fuel on board. the rocket is coasting through space at 159 m/s and needs to boost its speed to 254 m/s; it does this by firing its engines and ejecting fuel at a relative speed of 688 m/s until the desired speed is reached. how much fuel is left on board after this maneuver?

To find the remaining fuel after the rocket's maneuver, we use the rocket equation and the principles of conservation of momentum to calculate the mass of the rocket and the remaining fuel after attaining the desired speed. Subtracting the mass of the rocket itself gives us the mass of the remaining fuel.

Explanation:

The calculation of the remaining fuel after a rocket maneuver involves the concepts of conservation of momentum and the rocket equation. To reach the desired velocity, the rocket needs to eject a certain amount of fuel at a specific speed. Given that the initial speed of the rocket is 159 m/s, and it needs to boost to 254 m/s, using the rocket equation (Δv = ve * ln(m0/m)), where Δv is the change in velocity (254-159 = 95 m/s), ve is the relative speed of ejected fuel (688 m/s), and m0 and m are the initial and final masses of the rocket system, we can calculate the final mass (m).

Substituting these values into the rocket equation, we solve for m, which provides the mass of the rocket plus remaining fuel. Subtracting the mass of the rocket itself (2140 kg) from this result gives the mass of the remaining fuel, therefore answering the question.

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