During testing for the original astronauts a centrifuge was used to propel them

Question

During testing for the original astronauts a centrifuge was used to propel them up to a 20 g normal acceleration. the astronaut sat facing into the center of the ring. Answer the following questions.
1. If the radius is 5 meters how fast is the astronaut traveling at peak speed?
2. what tangential acceleration was used if it took 1.25 minutes to achieve this speed?
3. while at peak speed, the astronaut throws a ball directly forward relative to him at 4 m/s. What is the balls velocity relative to the ground at that moment?
4.explain what would happen to the ball just after it has been released.
5.the astronaut is held at speed for 2 mins then brought to rest over 3 mins. How many total revolutions will he complete?

Explanation / Answer

1) centripetal acceleration = v^2/r = 20g = 196

v = (196*5) = 31.304m/s

2) a = v/t = 31.304/(1.25*60) = 0.417m/s2

3) the ball velocity towards the centre = 4m/s and astronaut's velocity = 31.304m/s

Therefore ball's velocity reative to ground = (31.304^2 + 4^2) = 31.557m/s

4) the ball goes in a direction which makes an angle tan-1(33.304/4) to the incident line

5) The astronaut us held at that speed for 2mins=120seconds

Total distance travelled = 31.304*120 = 3756.48m

Number of revolutions = 3756.48/(2**r) = 119.55

While decelerating, distance travelled = 31.304(180) - 0.5*31.304*180 = 2817.36m

Number of revolutions = 2817.36/(2r) = 89.66

Therefore total number of revolutions = 89.66+119.55 = 209.21

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