The height above the ground of a rider on a large Ferries wheel can be modelled by h(t)=10sin(2pi/30 t) + 12, where h is the height above the ground, in metres and t is the time in seconds. What is the maximum height reached by the rider and when does it occur?

I know the max height is 22 m, but when does it occur?

To find when the maximum height occurs, we need to determine the value of t that corresponds to the maximum value of the function h(t).

The given function is h(t) = 10sin(2π/30 t) + 12, where h represents the height above the ground and t represents the time in seconds.

Since sin(x) has a maximum value of 1, we know that the maximum height occurs when sin(2π/30 t) is equal to 1.

Using the unit circle and the fact that sin(x) = 1 when x = π/2, we can set 2π/30 t equal to π/2 and solve for t.

2π/30 t = π/2

Simplifying, we can cancel the π's and multiply both sides by the reciprocal of 2/30, which is 30/2:

t = (π/2) * (30/2)

t = 15 seconds

Therefore, the maximum height of 22 meters occurs at t = 15 seconds.