posted by Anonymous

A ferris wheel has a radius of 13 m. It rotates once every 24 seconds. A passenger gets on at the bottom
of the wheel from a ramp which is one metre above ground level.

a) If the height of the passenger is measured from the ground, determine an equation for the height of the
passenger as a function of time in the form of h(t)= acos(bt)+d
b) To the nearest metre, find the height of the passenger after 55 seconds.

1. Reiny

2π/k = period
2π/k = 24
k = 2π/24 = π/12 <---- that's the b of your equation.
also we know a = 13

the minimum of this graph is -13, we want the min to be +1, so we have to raise it 14 units

h(t) = 13 cos (π/12 t) + 14

I would have started with a sine function, rather than a cosine function, since the sine starts at 0 when t = 0 and would be increasing.
The cosine curve would start at 1 when t = 0
So we have to move our cosine function horizontally to achieve this.
Let's see what we have so far

http://www.wolframalpha.com/input/?i=h(t)+%3D+13+cos+(%CF%80%2F12+t)+%2B+14

if we translate our curve 12 units to the right, we get:
http://www.wolframalpha.com/input/?i=h(t)+%3D+13+cos+((%CF%80%2F12)(t+-+12)))+%2B+14

so h(t) = 13cos ( (π/12)(t-12) ) + 14

checking:
when t = 0 , h(t) = 13 cos (-π) + 14 = 1 --> bottom
when t = 6 , h(6) = 13cos(-π/2)+14 = 14 --> half-way up
when t = 12, h(12)=13cos(0)+14 = 27 --> the top
when t= 18, h(18) =13cos(π/2)+14 = 14
when t=24, h(24) = 1

equation is good,

b) when t = 55
wheel has gone 55/24 = 2 + 7/24 periods
so it would be in the same position as it would be at 7 seconds

h(7) = 13cos (-5π/12) + 14
= appr 17.4 m high

## Similar Questions

1. ### trig question

A Ferris wheel has a deameter of 50m. The platform at the bottom, where you load the ferris wheel, is 3 m above the ground. The Ferris wheel rotates three times every two minutes. A stopwatch is started and you notice you are even …
2. ### math

a ferris wheel has a radius of 8m and rotates every 12 hrs. THe bottom of the ferris wheel is 1m above the ground. draw a graph describing how a person's height above the ground varies with time. Find an qeation for your graph.
3. ### math

A ferris wheel has radius of 25 m and its centre is 27 m above the ground. It rotates once every 40 seconds. Sandy gets on the ferris wheel at its lowest point and the wheel starts to rotate. Determine a sinusodial equation that gives …
4. ### physics

A Ferris wheel with radius 8.8 m rotates at a constant rate, completing one revolution every 34.6 s. Suppose the Ferris wheel begins to decelerate at the rate of 0.212 rad/s2 when a passenger is at the top of the wheel. Find the magnitude …
5. ### Trigonometry

A carnival Ferris wheel with a radius of 7 m makes one complete revolution every 16 seconds. The bottom of the wheel is 1.5 m above the ground. The ride starts at the bottom. Find the sinusoidal function that models this Ferris wheel …
6. ### Math (Trig)

a ferris wheel has a radius of 10m and is one meter above the ground. If the ferris wheel makes 1 revolution every 20 seconds, write an equation that gives the height above the ground of a person on the ferris wheel as a function of …
7. ### Math

The rim of the London Eye (a 135m diameter ferris wheel) moves 26 cm/sec, slow enough for passengers to safely get on the wheel from the platform (2 meters above ground level) without stopping the wheel at the bottom of its rotation. …