Pre-Calculus math problem with trigonometric Functions?

Question

Hi all, here is a challenging problem that needs solving...Please don't tell me that this is my homework and that I need to do it myself because this is NOT my homework. I'm serious.

1) A Ferris wheel makes one complete turn every 20 sec. The lowest the chairs can get is 8 feet off the ground, and the radius of the ferris wheel is 25 feet. A rider's height, h, above the ground can be modeled by the equation

h = a sin wt + k, where h and k are given in feet and t is given in seconds.


what is the value of a?
what is the value of k?
What is the value of w?



2) Jacob and Emily ride a Ferris wheel. The wheel has a 16meter diameter and turns at 3rpm with its lowest point 1m above the ground. Assume that Jacob and emily's hight h above the ground is a sinusoidal function of time t (in seconds) where t = 0 represents the lowest point of the wheel.


thanks all, and everybody who gets this right will be awarded points (I will make it so!)

Answer 1

A is the radius of the circle. (25 in this case)
K is the height of the center of the circle i think (33)
W is the angular velocity or similar (im thinking this would be 1/20)


god i havent done this stuff in a long time, and dont feel like putting much thought into it

Answer 2

In 1) you have then
2(pi) = 20w ----> ....
a = 25
-8 = a*(-1)+ k ----> .....
[as the lowest for f(x)=sinx is (-1)]

In 2) the radius is 16/2 and you have
h = 8sin(wt+b) + k
and the minimum is for t=o then
h_min =8sin(b) + k = -1 (edited) --->
(b= - pi / 2 and k= 7)
With this, you to find w

Answer 3

1) a=amplitude
a=high point - ((high point - lowest point)/2)
a=58-((58-8)/2)=25

w=frequency
w=2pi/20=pi/10

k=vertical shift
k=(high point - low point)/2
k=(58-8)/2=33

2) h=8sin((pi/10)t+5) + 9 <-- were you looking for the equation?

i hope it's right. i just learned this in class and my teacher would kill me if it's wrong. =]

Answer 4

THIS is YOUR homework! you NEED to do it yourself because this IS your homework! I'M DEAD SERIOUS!!