Question

A carnival Ferris wheel with a radius of 9.5 m rotates once every 10 seconds. The bottom of the wheel is 1.2 m above the ground. Find the equation of the sine function that gives the rider’s height above the ground, in metres, as a function of the time, in seconds, with the rider starting at the bottom of the wheel.

Answer 1

The equation of the sine function that gives the rider's height above the ground as a function of time is y = 9.5 sin((2π/10)t) + 1.2.

Step-by-step explanation:

To find the equation of the sine function that gives the rider's height above the ground as a function of time, we can use the standard form of a sine function:

y = A sin(Bx + C) + D

Where:

• A is the amplitude of the function
• B is the period of the function
• C is the phase shift of the function
• D is the vertical shift of the function

In this case, since the rider starts at the bottom of the wheel and the bottom of the wheel is 1.2 m above the ground, the vertical shift (D) is 1.2 m.

The period of the function (B) can be determined by the time it takes for one complete revolution, which is 10 seconds.

The radius of the Ferris wheel (9.5 m) is equal to the amplitude (A) of the function. The phase shift (C) is 0 because the rider starts at the bottom.

Therefore, the equation of the sine function that gives the rider's height above the ground as a function of time is:

y = 9.5 sin((2π/10)t) + 1.2