Question

Xavier is riding on a Ferris wheel at the local fair. His height can be modeled by the equation H(t) = 20cosine of the quantity 1 over 15 times t + 30, where H represents the height of the person above the ground in feet at t seconds.

Part 1: How far above the ground is Xavier before the ride begins?
Part 2: How long does the Ferris wheel take to make one complete revolution?
Part 3: Assuming Xavier begins the ride at the top, how far from the ground is the edge of the Ferris wheel, when Xavier's height above the ground reaches a minimum?

You must show all work.

Answer 1

i have the first part @jdoe0001 @nincompoop @Australopithecus

Answer 2

i believe the first part is 50 feet

Answer 3

\[h(t)=20\cos (1/15t)+30\] Is this the equation?

Answer 4

pi/15*t @nelsonjedi

Answer 5

\(\large \bf h(t)=20cos\left(\frac{\pi}{15t+30}\right)?\)

Answer 6

or \(\bf \large h(t)=20cos\left(\frac{\pi}{15t}\right)+30?\)

Answer 7

hmm \(\large \bf h(t)=20cos\left(\frac{\pi}{15t}+30\right)?\)

Answer 8

\[h(t)=20\cos( \frac{ \pi }{ 15 }t)+30\]

Answer 9

ok hmm ok so... what did you get for part 1 anyway?

Answer 10

50

Answer 11

insert 0 for t

Answer 12

hmm ok... so to find how long it takes, we can find how long is the function's period
since a period is how long it went from the ground and came back down to the original point

thus \(\bf h(t)=20cos\left({\color{brown}{ \frac{\pi}{15}}}t\right)+30\qquad period\implies \cfrac{regular\ period}{{\color{brown}{ B}}}\to \cfrac{2\pi}{{\color{brown}{ \frac{\pi}{15}}}}\)

Answer 13

ok

Answer 14

for part 3

I think is just finding what h(t) is 3/4 of the way or 3/4 of the period
so... whatever the period is... 3/4 of that of the way... will be at