the height of a seat on a ferris wheel can be modeled as h(t)=48 sin(π/30t + 3π/2)+53, where t is time in…

the height of a seat on a ferris wheel can be modeled as h(t)=48 sin(π/30t + 3π/2)+53, where t is time in seconds and h(t) is height in feet. how far off the ground is a seat when it is at the top of the ferris wheel? a. 101 feet b. 53 feet c. 106 feet d. 96 feet

the height of a seat on a ferris wheel can be modeled as h(t)=48 sin(π/30t + 3π/2)+53, where t is time in seconds and h(t) is height in feet. how far off the ground is a seat when it is at the top of the ferris wheel? a. 101 feet b. 53 feet c. 106 feet d. 96 feet

Answer

Explanation:

Step1: Recall sine - function property

The maximum value of the sine function $y = \sin(x)$ is 1.

Step2: Substitute maximum value of sine into $H(t)$

We have $H(t)=48\sin(\frac{\pi}{30}t+\frac{3\pi}{2}) + 53$. When $\sin(\frac{\pi}{30}t+\frac{3\pi}{2}) = 1$, we calculate $H(t)$. $H(t)=48\times1 + 53$.

Step3: Calculate $H(t)$

$H(t)=48 + 53=101$.

Answer:

A. 101 feet