Question

Amelia is on a ferris wheel that has a radius of 40m. She starts in a cart at the bottom of the wheel which is 10m off the ground. It takes 45 seconds to complete one full rotation.

Which function models Amelia's height, t seconds since she got on the ride?

Answer 1

h(t) = 40 cos(π/22.5 t) + 10.

Explanation:

The function that models Amelia's height, h, at time t can be written as:

h(t) = r cos(ωt) + a

where:

r is the radius of the ferris wheel (40 m)

a is the initial height of the cart above the ground (10 m)

ω is the angular velocity of the ferris wheel, which is equal to 2π divided by the time for one complete rotation (T)

T is the time for one complete rotation, which is given as 45 seconds

To find ω, we can use the formula:

ω = 2π/T

ω = 2π/45

ω = π/22.5

Substituting the values into the function, we get:

h(t) = 40 cos(π/22.5 t) + 10

Therefore, the function that models Amelia's height, h, at time t since she got on the ride is h(t) = 40 cos(π/22.5 t) + 10.