A Ferris wheel with a radius of 9.9 m rotates at a constant rate, completing one revolution every 36 s. Suppose the Ferris wheel begins to decelerate at the rate of 0.19 rad/s² when the passenger is at the top of the wheel.
Find the magnitude of the passenger's acceleration at that time.

9.68 m/s2

Explanation:

If it completes 1 revolution, or 2π for every 36 seconds, then its angular speed ω is 2π/36 = 0.1745 rad/s

So the centripetal acceleration would be

The tangential acceleration is:

When the passenger is on top of the wheel, the tangential acceleration is horizontal, while centripetal acceleration is vertical, acting upward, gravitational acceleration g is 9.8 m/s2 acting downward. The total vertical acceleration is 0.3 - 9.8 = -9.5 m/s2

So the magnitude of the total acceleration consisting of horizontal and vertical components is: