A woman rides a carnival Ferris wheel at radius 16 m, completing 4.5 turns about its horizontal axis every minute. What are (a) the period of the motion, and the magnitude of her centripetal acceleration at (b) the highest point and (c) the lowest point

a)13.33s

b)at highest point, the centripetal acceleration has its direction at downward path towards the center of the circular path, and the radius vector has its direction upward. Then acceleration=3.555m/s^2

c)c)at lowest point the centripetal acceleration has its direction upward towards the center of the circular path, and the radius vector has its direction downward Then acceleration=3.555m/s^2

Explanation

a)number of turns= 4.5

radius= 16m

We know that the period is the time taken by the wheel to complete one turn which can be calculated using below expresion

T= t/n

Where T= period of motion

t= Time taken by the wheel to finish n turns where our n= 4.5

T= (1×60)/4.5= 13.33s

Hence the period is 13.33s

Then the speed of the woman v= 2πr/T

v= (2×π×16)/13.33

v=7.5417m/s

b)at highest point, the centripetal acceleration has its direction at downward path towards the center of the circular path, and the radius vector has its direction upward.

a= v^2/r

Where r= radius

v= speed of the woman= 7.5417m/s

a=(7.5417m/s)^2/16

a=3.555m/s^2

The centripetal acceleration and radius vector are in opposite direction

c)at lowest point the centripetal acceleration has its direction upward towards the center of the circular path, and the radius vector has its direction downward

The magnitude of the acceleration is calculated below

a= v^2/r

Where r= radius

v= speed of the woman= 7.5417m/s

a=(7.5417m/s)^2/16

a=3.555m/s^2

neither accurate nor precise.