Answer:
at time, t = 8 seconds and t = 24 seconds Ferris Wheel be 53 feet above the ground
Step-by-step explanation:
Data provided in the question:
height in feet above ground of a seat on the wheel at time t seconds is
modeled as
h(t) = [tex]53 + 50\sin((\frac{\pi t}{16} - \frac{\pi}{2})[/tex]
now,
at height 53 above the ground, we get the equation as:
53 = [tex]53 + 50\sin(\frac{\pi t}{16} - \frac{\pi}{2})[/tex]
or
[tex]50\sin(\frac{\pi t}{16} - \frac{\pi}{2})[/tex] = 53 - 53
or
[tex]\sin(\frac{\pi t}{16} - \frac{\pi}{2})[/tex] = 0
also,
sin(0) = 0
and,
sin(Ï€) = 0
therefore,
[tex](\frac{\pi t}{16} - \frac{\pi}{2})[/tex] = 0
or
[tex]\frac{\pi t}{16} = \frac{\pi}{2}[/tex]
or
t = 8 seconds
and,
[tex](\frac{\pi t}{16} - \frac{\pi}{2})[/tex] = π
or
[tex]\frac{\pi t}{16}= \pi + \frac{\pi}{2}[/tex]
or
[tex]\frac{\pi t}{16}= \frac{3\pi}{2}[/tex]
or
t = 24 seconds
Hence,
the at time, t = 8 seconds and t = 24 seconds Ferris Wheel be 53 feet above the ground
