We have the function for the height:
[tex]h(t)=58+50\sin (\frac{\pi}{2}t-\frac{\pi}{2})[/tex]
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:
[tex]h_{\max }=58+50\cdot1=58+50=108[/tex]
Answer: the maximum height is 108 feet.
