5 pts A ferris wheel is 70 meters in diameter and boarded at

(5 pts) A ferris wheel is 70 meters in diameter and boarded at its lowest point (6 O\'Clock) from a platfomm which is 20 meters above ground. The wheel makes one full rotation every 16 minutes, and at time t0you are at the highest point on the ferris wheel (at 12 OClock). Let h = f(t ) denote your height above ground in meters after t minutes (a) What is the period of the function h = f(t)? period = Include units in your answer (b)What is the midline of the function h = f(t)? Include units in your answer. (c) What is the amplitude of the function h-f(t) amplitude = Include units in your answer d) Consider the six possible graphs of h =) below Be sure to enlarge each graph and carefuly read the labels on the axes in order distinguish the key features of each graph Which (if any) of the graphs A-F represents two full revolutions of the ferris wheel plus the additional partial revolution needed to retum to the loading platfom of the feris wheel described above? WNAW Wite a function ft) that describes the height of the passenger as a function of time f(t)- 145

Solution

comparing with y=Acos(Bt) +h

(a)

period =16 minutes

2_/B=16

=>B=_/8

(b)

midline ,h=20+(70_/2)

midline ,h=55 meters

(c)

amplitude,A= (70_/2)

amplitude,A= 35 meters

(d)

graph E

height of the passenger as a function of time,f(t) =-35cos((_/8)t) +55