To prepare for the g-forces of space launch, an astronaut is training on a centrifuge where is apparent weight is 7.6 times his normal weight mg. The centrifuge spins the astronaut in a horizontal circle of radius 4.12 m at constant speed v while the Earth's gravity pulls him down at 9.8 m/s^2. The astronaut's seat is inclined to stay perpendicular to his apparent weight. Calculate the centrifuge's rotational speed v. Answer in units of m/s.