Question

A person’s height, in feet above the ground, on a Ferris wheel can be modeled using the equation: h(t) = -45 cos(πt/7) + 52. How long does it take for the rider to reach maximum height? What changes when the Ferris wheel has a larger radius?

Answer 1

To find the time it takes for the rider to reach maximum height, we need to find when the derivative of the height function h(t) is equal to 0.

h'(t) = 45π/7 sin(πt/7)

Setting h'(t) equal to 0 gives:

45π/7 sin(πt/7) = 0

sin(πt/7) = 0

πt/7 = nπ, where n is an integer

t = 7n, where n is an integer

So, the rider reaches maximum height every 7 seconds.

When the Ferris wheel has a larger radius, it means the amplitude of the cosine function in the equation will be larger. This means the difference between the maximum and minimum height the rider reaches will be greater, but the time it takes for the rider to reach the maximum height will remain the same.