Question

matthew takes a trip to an amusement park and rides a ferris wheel. the graph below shows the height, in feet above the ground, of his car over time, t, measured in minutes. what is the amplitude and what does it represent in this context? height of the car (in feet) time (in minutes)

Explanation:

Step1: Recall amplitude definition

The amplitude of a periodic - function is half the difference between the maximum and minimum values.

Step2: Identify maximum and minimum values

From the graph, the maximum height of the car is $h_{max}=360$ feet and the minimum height is $h_{min}=25$ feet.

Step3: Calculate the amplitude

The amplitude $A=\frac{h_{max}-h_{min}}{2}=\frac{360 - 25}{2}=\frac{335}{2}=167.5$ feet. In the context of the Ferris - wheel ride, the amplitude represents the maximum vertical distance the car moves above or below the mid - height of its motion.

Answer:

The amplitude is $167.5$ feet. It represents the maximum vertical distance the car moves above or below the mid - height of its motion on the Ferris wheel.