A device for training astronauts and jet fighter pilots is designed to rotate the trainee in a horizontal circle of radius 11.0 m. if the force felt by the trainee is 7.80 times her own weight, how fast is she rotating? express your answer in both (a) m/s and (b) rev/s.

Refer to the diagram shown below.

v = the tangential velocity

r = 11.0m, the radius

mg = the weight of the astronaut.

The centripetal force is 7.80times the astronaut's weight.

Therefore

(mv²) / r = 7.8mg

v² = 7.8rg = 7.8 * (11.0 m) * (9.8 m/s²) = 840.84 (m/s) ²

v = 29 m/s

The angular velocity is

ω = (29 m/s) / (11.0 m) = 2.6364 rad/s

= (2.6364 rad/s) * (1/2π rev/rad)

= 0.4196 rev/s

Answer: 29 m/s, 0.42 rev/s