Maths
posted by Raina .
A ferris wheel has an axle standing 38m off the ground and a radius of 35m. The wheel takes 5 minutes to complete one revolution. The wheel moves in clockwise motion and you are sitting in one of the carriages which is horizontally in line with the axle, moving upwards.
Form an equation that models the displacement of the carriage from the axle one revolution.

The height of the axle does not matter.
Let the axle be at (0,0)
Assuming that at t=0 the carriage is horizontally in line with the axle,
x(0) = 35
y(0) = 0
The amplitude is 35.
The period is 5, so we are looking at
y(t) = 35sin(2pi/5 t)
x(t) = 35cos(2pi/5 t)
x^2 + y^2 = 35^2 
TASK 1:
Consider that it is sunset with the sun’s rays parallel to the rim of the wheel, so that the wheel’s shadow is falling on to the vertical wall of the building.
The car’s shadow moves up and down the wall. You may like to use a wheel and torch to experience what this may look like.
I. Form an equation that models the displacement of the carriage from the axle one revolution. (B maps) (State any assumptions that you have made and the effects they have on the overall result)(ASSUMPTIONS AND EFFECTS MAPS A OR B)
II. Sketch this equation with the aid of technology. State the points of interest on this graph. (C KAPS)
III. Consider vertical velocity of the carriage.
When does the shadow appear to be :
a. Stationary
b. Travelling the fastest upwards
c. Travelling the fastest downwards (C KAPS)
IV. Manually sketch the vertical velocity of the carriage. (This does not need to be accurate, a sketch indicating the general shape of the curve is sufficient)(C KAPS)
V. State the period, amplitude and possible equation for the curve. (C KAPS)
VI. Calculate the derivative of the displacement function and compare this to the vertical velocity function graphically and verbally. (COMPARISON MAPS C)
TASK 2: KAPS AND MAPS
1. Find the equation that models the height of the car over time. (B MAPS)
2. Use this equation to find:
a. The height of the carriage after 2 minutes into the ride and the direction of its motion. (KAPS)
b. The times (minutes and seconds) during one revolution, when the carriage is 20m off the ground.(KAPS)
3. Find the equation that models the height of the car, if we start our analysis one minute into the ride. (B MAPS)
4. Using the original equation (starting at time zero), find an equation to represent height, if the carriage now takes 10 minutes for one revolution. (B KAPS)
5. Assuming that the sun is now directly above your carriage so that the shadow of the carriage you are in is directly beneath you. Write the equation that models the displacement that the car’s shadow is from the shadow of the axle. (STATE THE STRENGTHS AND LIMITATIONS OF THE DEVELOPED MODEL) (A LEVEL)
TASK 3: KAPS AND MAPS
1. The equations for height and velocity from previous tasks were expressed using degrees. Using fractions, rewrite them using radians. (KAPS)
2. Find the maximum upward velocity of the wheel and the time this occurs within one revolution. (KAPS/MAPS)
3. Using the ‘rule’ for speed, calculate the constant speed of your carriage and then compare this with the maximum upward velocity.( KAPS) (COMPARISON MAPS C)
Throughout this entire EMPS, there are opportunities to justify your responses and the reasonableness of them. Data is modeled regularly and you have an opportunity to state the strengths and limitations of each of them. Ensure your responses are logical, coherent and concise, to ensure that you have the opportunity to receive a high grade. Follow the criteria to achieve.
Respond to this Question
Similar Questions

Physics
Fairgoers ride a Ferris wheel with a radius of 5.00 {\rm m} . The wheel completes one revolution every 31.5 s What is the average speed of a rider on this Ferris wheel? 
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 … 
math
the maximun height of a ferris wheel is 35m. the wheel takes 2 mins to make one revolution. passengers board the ferris wheel 2m above the ground at the bottom of the rotation. a. write an equation to model this b. how high is the … 
Maths
Consider the Ferris wheel above. It has an axle standing 38m off the ground and a radius of 35m. The wheel takes 5 minutes to complete one revolution. The wheel moves in clockwise motion and you are sitting in one of the carriages … 
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. … 
Pre Calculus 12
Modelling with sine/cosine A Ferris wheel has a diameter of 30m. The bottom of the wheel is 1.5m off the ground it takes 3.5min to make one complete revolution. a person gets on ferris wheel at its lowest point at time = 0. write an … 
trig
1. A Ferris wheel with a radius of 7m makes one complete revolution every 16 s. The bottom of the wheel is 1.5m above ground. a)Find the equation of the graph b)predict how the graph and the equation will change if the Ferris wheel … 
Precal
Suppose that you are sitting in a chair on a Ferris wheel that has a diameter of 120 feet that is boarded 6 feet above the ground at the 6 o’clock position. If the Ferris wheel moves in a counterclockwise direction and makes one … 
calculus
Eric is standing on the ground, a distance of 70 ft from the bottom of Ferris wheel that has a 20 ft radius. His arm is at the same height as the bottom of the Ferris wheel. Janice is on Ferris wheel which makes one revolution counter … 
Physics
A particular Ferris wheel takes you through one complete revolution every 25.3 seconds. If the radius of the Ferris wheel is 10.4 m, and your mass is 63.3 kg, calculate: (a) Your apparent weight, in N, when you are at the top of the …