Question

The National Aeronautics and Space Administration (NASA) studies the physiological effects of large accelerations on astronauts. Some of these studies use a machine known as a centrifuge. This machine consists of a long arm, to one end of which is attached a chamber in which the astronaut sits. The other end of the arm is connected to an axis about which the arm and chamber can be rotated. The astronaut moves on a circular path, much like a model airplane flying in a circle on a guideline. The chamber is located 15 m from the center of the circle. At what speed must the chamber move so that an astronaut is subjected to 6.9 times the acceleration due to gravity?

Answer 1

v^2 /R = horizontal acceleration
If you just mean the horizontal problem
then
v^2 = R * 6.9 g = 15 * 6.9 * 9.81 = 1015
v = 31.9 m/s

However I ignored the 9.81 m/s^2 down that is still present
9.81 down and v^2/R horizontal
sqrt (9.81^2 + v^4/R^2) = 6.9 * 9.81