Problem 1 of 3
A ferris wheel at an amusement park has riders get on at the bottom of the wheel which is 3 meters above the ground. The highest point of the ride is 21 meters above the ground and it takes 48 seconds to make a one complete revolution.
(a) Write two equations, one sine and one cosine, that models the height of a rider over time beginning from when they first start the ride.
(b) How long would it take a rider to pass through an angle of 2π/3 radians?
(c) How long during each revolution is a rider higher than 10 meters above the ground?
Solution
a) H(t)= 3sin[(2π/48(t+0)]+12 and H(t)= -3cos[(2π/48)(t-12)]+12
b) it would take about 9 + 48 = 57 seconds to pass through the angle of 2π/3 radians
c) 10 = 3sin[(2π/48(t)]+12
let [2π/48(t)]=x
10=3sinx+12
-2=3sinx
sinx=-2/3
(48/2π)[2π/48(t)]= -2/3(48/2π)
t=-2/3(48/2π)
^^ i think..need my notes and calculator
still working on this...don't take..hehe sorry got no calculator on me right now..ill be back tomorrow =D
Problem 2 of 3
Determine the general solution algebraically. (Solve over the set of real numbers and write your answer accurate to at least 3 decimal places.)
Solution
Problem 3 of 3
A sinusoidal curve has a minimum point at (-π/3, -5) and the closest maximum point to the right is (π/6, 3).
(a) Determine an equation of this curve.
(b) Sketch the graph.
Solution