Final answer:
A suitable equation for the height of a passenger on a Ferris wheel in terms of time is h(t) = 10 - 10 · cos(ωt), where ω is the angular velocity of the Ferris wheel.
Step-by-step explanation:
The question involves determining an equation for the height of a passenger on a Ferris wheel with respect to time. This is a classic application of trigonometric functions to model periodic motion. Given that the Ferris wheel has a radius of 10 meters and completes 3 rotations in 6 minutes, one can derive the equation based on the sinusoidal motion of the passenger on the Ferris wheel.
Firstly, we determine the angular velocity (ω) of the Ferris wheel, which is the rate at which it rotates. Since it completes 3 turns in 6 minutes (or 360 seconds), the angular velocity in radians per second is calculated as ω = (3 turns * 2π radians/turn) / 360 seconds.
Then, using the sine function to model the height (h) with respect to time (t), the equation can be written as h(t) = R - R · cos(ωt), where R is the radius of the Ferris wheel, and t is time in seconds. Hence, the equation for the height of the passenger at time t is h(t) = 10 - 10 · cos(ωt).