Question

Suppose you want to model the height of a rider on a Ferris wheel as a function of time, t, in minutes. If the rider is at the bottom of the Ferris wheel at t = 0 minutes, which of the following would be easiest to use? Option 1: The cosine function unreflected Option 2: The sine function unreflected Option 3: The cosine function reflected about its midline Option 4: The sine function reflected about its midline

Answer 1

The easiest function to model the Ferris wheel rider starting at the bottom at t = 0 is the cosine function unreflected, as it naturally starts at a minimum when unreflected, fitting the initial condition without any need for adjustments.

Step-by-step explanation:

In modeling the height of a rider on a Ferris wheel as a function of time, we must consider the rider's starting position. At t = 0 minutes, the rider is at the bottom of the Ferris wheel. The easiest function to use would be the cosine function unreflected (Option 1). This is because the standard cosine function starts with a maximum at the beginning of its cycle, but since we want the rider to start at the bottom, we need a cosine function that starts at a minimum. Since the negative cosine function begins at its minimum value, it models the situation accurately without the need for vertical flipping. The initial conditions at t = 0 minutes for a sine or cosine function involve the starting height of the rider (the function value), the initial velocity of the rider (the slope of the function), and the initial acceleration of the rider (the second derivative of the function).