Question

brianna 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? height of the car (in feet)

Explanation:

Step1: Identify maximum and minimum heights

The maximum height of the Ferris - wheel car is 170 feet and the minimum height is 20 feet.

Step2: Use amplitude formula

The formula for the amplitude $A$ of a periodic function (like the height of the Ferris - wheel car over time) is $A=\frac{\text{Max}-\text{Min}}{2}$. Here, $\text{Max} = 170$ and $\text{Min}=20$. So $A=\frac{170 - 20}{2}$.

Step3: Calculate the amplitude

$A=\frac{150}{2}=75$. In the context of the Ferris - wheel, the amplitude represents the maximum distance the car moves above or below the mid - height of its motion. The mid - height of the Ferris - wheel is $\frac{170 + 20}{2}=95$ feet, and the amplitude of 75 feet is the maximum vertical displacement from this mid - height position.

Answer:

The amplitude is 75 feet. It represents the maximum distance the Ferris - wheel car moves above or below the mid - height of its motion.