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.
sure hope they have a rest-room on that ferris wheel if it takes 12 hours to make one rotation.
anyway, I know that the basic shape could be y = 8sin(pi/6)t.
since period = 2pi/k for y = sin kt
and 2pi/k = 12, so k=pi/6
I then shifted this vertically by 9 m to have the person 1 m above the x-axis at the minimum height
But I want him to be only 1 m high when t=0 so I shifted the graph to the right by 3 hours
which gave me y = 8 sin (pi/6)(t - 3) + 9
testing:
t=0 y = 1
t=3 y = 9
t=6 y = 17 , maximum height
t=9 y = 9
t= 12 y = 1, it works!!!
i don't get it. the answer is right but how do you know to shift the graph right by 3 hrs?
To draw a graph describing how a person's height above the ground varies with time on a Ferris wheel, we need to understand the motion of the wheel and how it relates to the height of the person.
The Ferris wheel completes one full rotation every 12 hours, which means it takes 12 hours to travel 360 degrees. Assuming the Ferris wheel starts at the bottom, we can create a graph that shows the height of the person above the ground as the wheel rotates.
Here's how we can do it:
1. Set up the x-axis to represent time in hours and the y-axis to represent the height above the ground in meters.
2. Divide the x-axis into 12 equal intervals, each representing one hour.
3. At t = 0 (initial time), the person is at the bottom of the Ferris wheel, 1 meter above the ground.
4. As time progresses, the person moves upwards as the Ferris wheel rotates. At t = 0.5 hours, the person would be at the highest point, 9 meters above the ground (radius + height above the ground).
5. As time continues, the person descends back down to the bottom, reaching a height of 1 meter again at t = 1 hour.
6. Repeat this cycle for each interval of 1 hour on the x-axis, creating a wave-like pattern on the graph.
The equation for the graph can be written as:
h(t) = 8sin(2πt/12) + 1
Where h(t) represents the height above the ground in meters at time t in hours. The term 8sin(2πt/12) represents the vertical displacement due to the rotation of the Ferris wheel, and the "+ 1" accounts for the initial height of 1 meter above the ground.
Plotting this equation on the graph will give you the desired representation of how a person's height above the ground varies with time on the Ferris wheel.