Question

There is a new Ferris wheel opening this year at Frontier city. The ride lasts for 18 minutes, tickets are just $2, and the height in feet of a car after t seconds can be modeled
by the trigonometric function h(t)=48sin(2.1t-1.3)+55. Determine the amplitude of h(t) and interpret what the amplitude represents in this context.

Answer 1

Answer:

• Amplitude = 48
• Interpretation: The vertical distance from the center line to either the highest point or the lowest point is 48 feet. It represents half the total vertical distance from peak to valley.

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Explanation:

The facts "The right lasts for 18 minutes" and "tickets are just $2" are not relevant to this question.

All we care about really is the h(t) function.

The general sine function is

y = A*sin(B(x-C)) + D

where

• |A| = amplitude
• B is used to find the period T = 2pi/B
• C is the horizontal phase shift
• D is the vertical shift and y = D is the center line

Here we have A = 48 so |A| = |48| = 48 is the amplitude. If you graphed the h(t) function, you would find that y = 55 is the center line and y = 55+48 = 103 is the highest y value possible, while y = 55-48 = 7 is the lowest y value possible.

In short, the Ferris wheel reaches the highest point of 103 feet and the lowest point of 7 feet off the ground.