Question

The height, (h(t)), in meters, of a passenger on a Ferris Wheel can be modeled by the equation (h(t) = 20sin(9°(t-10))+25), where (t) is the time in seconds. How long does it take for the Ferris Wheel to rotate 4 times?

a) 40 seconds
b) 80 seconds
c) 120 seconds
d) 160 seconds

Answer 1

To find how long it takes for the Ferris Wheel to rotate 4 times, we can use the period of the sine function and calculate the time. The answer is 80 seconds.

Step-by-step explanation:

To find how long it takes for the Ferris Wheel to rotate 4 times, we can set up an equation. We know that each rotation corresponds to a full cycle of the sine function, which has a period of 2π. Therefore, 4 rotations would correspond to 4 times the period.

Using the equation T = 2π/9°, where T is the period in seconds, we can calculate the period of the Ferris Wheel.

T = 2π/9 × 1° = 2π/9 × 1/360 × 360° = 2π/9 × 1/360 × 360 seconds = 80 seconds.

Therefore, it takes 80 seconds for the Ferris Wheel to rotate 4 times. The correct answer is b) 80 seconds.