Question

alexandra takes a trip to an amusement park and rides a ferris wheel. the graph below shows the height, in feet above the ground, of her car over time, t, measured in minutes. what is the amplitude and what does it represent in this context? (the graph has points (6.5, 280), (16.5, 280), (1.5, 10), (11.5, 10) and the height axis from 30 to 300, time axis from 0 to 20)

Explanation:

Step1: Identify max and min heights

Maximum height $h_{max}=280$ ft, Minimum height $h_{min}=10$ ft

Step2: Calculate amplitude

Amplitude = $\frac{h_{max}-h_{min}}{2}$
$\frac{280-10}{2}=\frac{270}{2}=135$

Step3: Interpret the amplitude

The amplitude is half the total vertical distance between the highest and lowest points of the Ferris wheel, so it represents the radius of the Ferris wheel (the distance from the center of the Ferris wheel to the car).

Answer:

The amplitude is 135 feet, and it represents the radius of the Ferris wheel (the vertical distance from the center of the Ferris wheel to Alexandra's car).