Mitch was about to give up but he finally did make it to her

Mitch was about to give up but he finally did make it to her house. Now they go to some place with a Ferris wheel that is built so that you are 2 ft off the ground at the lowest point and at the highest point you are 96 feet off the ground. You get on the Ferris wheel at its lowest point. It takes 235 seconds to go all the way around one time. Mitch wants to impress his date so he says he can model their height vs time as the Ferris wheel turns. She says he is full of it and full of himself. So he writes an equation down and says \"here it is, now let\'s get on and measure our height as we go around. If I am right you have to kiss me.\" She agrees and they get on the Ferris wheel. What equation should Mitch write down in order to get a kiss from this crazy girl who gave him completely messed up directions to her house? a. Sin(bx + c) + d a Cos(bx + c) + d a Tan(bx + c) + d

Solution

Height from ground = 2ft

heighest point = 96 ft

Diameter of wheel = 96 -2 = 94 ft

radius = 94/2 = 47 ft

mid line of trig function = 47 +2 = 49 ft

Time period = 235 sec

So, we select cos function :

y = 49cos(bx ) + 47

b = 2pi/ period = 2pi/235

So, y = -47cos(2pi*x/235) +49

So, lets verfiy whether is satiefies the height vs time graph:

t =0 ( when at bottom) y = -47 +49 = 2ft

at heighest point at t= 235/2 ; y = -47(cospi) +49 = 47 +49 = 96ft

So, it satisfies:

y = 49 - 47cos(2pi*/235)

a = -47 ; b = 2pi/235 ; c =0 ; d = 49