The Iorentz. Cup spaceship race is won by the pilot who can travel \(1.00 \times 10^{9} \mathrm{~m}\) in the shortest time interval. The rules state that the start and finish lines must be \(10^{9} \mathrm{~m}\) apart in the ships' reference frame, but the time interval is measured by an observer at rest in the Earth reference frame. There are many racing speeds you might try, such as \(0.420 c_{0}\) and \(0.980 c_{0}\) relative to the Earth reference frame, but trying a few combinations randomly makes you wonder if there is a better way than trial and error to decide on a strategy for this race.