Question

How high is a person from the ground when they are at the very top of the ferris wheel? Explain.

Answer 1

We have the function for the height:

`h(t)=58+50\sin ((\pi)/(2)t-(\pi)/(2))`

We have to find the maximum height.

If we look at the function, we see that the first term, 58, is fixed.

The second term is a factor of 50 multiplying a sine function.

This sine function will take values within -1 and 1.

So we can conclude that the maximum height will happen when the sine function takes a value of 1.

NOTE: This is the case because the term has a positive term (50). If not, it would be when the sine function takes a value of -1.

Then, if the sine function has a value of 1, the maximum height will be:

`h_(\max )=58+50\cdot1=58+50=108`

Answer: the maximum height is 108 feet.