A two-stage rocket has a total initial mass with the fuel of 4.5x106 kg is docked...

A two-stage rocket has a total initial mass with the fuel of 4.5x10⁶ kg is docked at rest at a space station. A total of 2.3x10⁶ kg of fuel is on board. The mission for the ship is to reach a planet that is located at a distance of 7.5x10¹⁰m away. The fuel is used at a constant rate of 800kg/s for both stages of the rocket. The exhaust velocity for the rocket's engines is 7500m/s (stage1) and 5000m/s (stage2). The mass of stage 1 (bottom half) is 0.75x10⁶kg without fuel after stage 1 is complete, stage 2 the ignites and accelerates the rocket until the fuel runs out. Assume all the motion takes place in one dimension and the gravitational force can be neglected.

1. The fuel allocated for the 1st stage is 1.5x10⁶kg but only 1.25x10⁶ kg is used. The rest remains on stage1. The fuel for the second stage is 0.8x10⁶kg. What is the speed of the rocket when stage 2 is complete?

2. How much faster or slower would you be going if you use all 2.3x10⁶kg of the rocket's fuel during stage 1 and didn't use the second stage?

3. Some fuel was left on stage 1 which is used to alter its velocity so that it can return to the space station. If you were to rotate stage 1 so that the exhaust point in the opposite direction, do you have enough fuel to return stage1 to the space station? What is the final velocity of the rocket? If not, what would the minimum exhaust velocity of stage one need to be adjusted to in order for the rocker to make it back?

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Expert Solution

genius_generous answered 1 year ago

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