We've just received an invitation to a grand party being thrown by an intelligent race on the planet Belbphextl which orbits Alpha-Centauri, the closest star to our sun. At a distance of just over four light-years, it takes light four years to traverse the distance. Fortunately, the party starts in 40 years and we can make it just in time if we can achieve a cruising velocity of 3 x 107 m/s. The United Earth Transport Services company (UETS) will build the ship.
We are sending ten delegates (frozen of course) in a modest automated suspended animation tank. With our best technology, we'll be able to reduced the total payload to a mere 10, 000 kg. (For comparison, the weight of a fully loaded 757 is over 200,000 kg!) What total mass of fuel will be required for the trip? Assume that UETS will assembled our low-tech propulsion rocket in deep space and that the earth's or sun's gravitational pull may be ignored in the calculations. The exhaust velocity for the engines is 3000 m/s. There is one more detail to take into consideration. We have promised the delegates that we'll bring them back to earth after the party and the Belbphextlians have no fuel.
Hardcopy entries should be submitted in class by noon on Monday of next week. Answers should be concise but complete.