Question

A Ferris wheel is designed in such a way that the height (h), in feet, of the seat above the ground at any time, t, is modeled by the function h(t)=60-55 sin((pi)/(10)t+(pi)/(2)) What is the maximum height a seat reaches?

Answer 1

The maximum height reached by a seat on the Ferris wheel, as given by the function h(t), is 115 feet.

Step-by-step explanation:

Calculating the Maximum Height of the Ferris Wheel Seat

The height (h) of a seat on a Ferris wheel above the ground at any time (t) is given by the function h(t) = 60 - 55 sin((pi)/(10)t + (pi)/(2)). To find the maximum height a seat reaches, we need to consider the properties of the sine function. The sine function oscillates between -1 and 1, so the expression 55 sin((pi)/(10)t + (pi)/(2)) will range from -55 to 55.

The maximum value of this expression is 55, which occurs when sin((pi)/(10)t + (pi)/(2)) equals 1. Therefore, the maximum height is obtained by subtracting the minimum of this expression (which is -55) from the constant term 60:

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• Maximum of -55 sin((pi)/(10)t + (pi)/(2)) = 55
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• Maximum height = 60 - (-55) = 115 feet

So, the maximum height reached by a seat on the Ferris wheel is 115 feet.