PLEASE HELP 50 PTS An 80.0 kg astronaut is training for accelerations that he will experience upon reentry to earth’s gravity from space. He is placed in a centrifuge (r = 25.0 m) and spun at a constant angular velocity of 10.0 rpm (revolutions per minute).
(a) Find the linear velocity of the centrifuge in m/s. Show your work

(b) Find the magnitude and direction of the centripetal acceleration when he is spinning at this constant velocity.

(c) How many g’s is the astronaut experiencing? (at constant velocity)

(d) Find the linear deceleration and torque required to bring the centrifuge (5000.0 kg) to a stop over a 5 minute time period.

Lake happy times contains 100 km3 of pure water. it is fed by a river at a rate of 50 km3/yr. at time zero, there is a factory on one shore of lake happy times that begins introducing a pollutant to the lake at a rate of 2km3/yr. there is another river that is fed by lake happy times at a rate that keeps the volume of lake happy times constant. this means that the rate of flow from lake happy times into the outlet river is 52km3/yr. in turn, the flow from this outlet river goes into another lake, lake sad times, at an equal rate. finally, there is an outlet river from lake sad times flowing at a rate that keeps the volume of lake sad times at a constant 100 km3 . (a) find the amount of pollutant in lake sad times at the end of 3 months. (b) at the end of 3 months, observers close the factory due to environmental concerns and no further pollu- tant enters lake happy times. how long will it take for the pollutant in lake sad times (found in part (a)) to be cut in half?