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?

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