Question

A Ferris wheel has a maximum height of 56 m and a minimum height of 14 m. It can make one rotation in 45 seconds. During the first rotation, when is the instantaneous rate of change of the height of a chair on the Ferris wheel 0, if it starts at the height of the Ferris wheel’s axle?

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Answer 1

The "instantaneous change of height at the height of the axle" is just a fancy expression for the linear velocity at that point. Velocity is distance/time and this distance at that point is the change of hight , that's why.

Now the diameter of the wheel = maximum height - minimum height = 42m

So the radius is = 42/2 = 21m

Distance traveled =

Time elapsed = 45s.

So velocity = 131.94/45 = 2.9 3m/s.

This is the instantaneous change of height at the height of the axle. The direction is upward if the rotation is anticlockwise and the chair starts from 3 O clock.