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 with the center of the ferris wheel, going down when the watch is at 4 seconds. write an equation that expreses your height as a function of elapsed time.
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h=28-25*sin((t-1/15)/(3pi))
t is in minutes
h is in meters
ma adre
45
To write an equation that expresses your height as a function of elapsed time, we need to consider the given information.
Let's break the problem down step by step:
1. The diameter of the Ferris wheel is 50m, which means the radius (r) is half of the diameter. So, r = 50m / 2 = 25m.
2. The platform at the bottom is 3m above the ground. Therefore, the center of the Ferris wheel is at a height of 3m + r from the ground. In this case, the height of the center would be 3m + 25m = 28m.
3. The Ferris wheel rotates three times every two minutes. This means it completes 3 revolutions in 2 minutes. To convert minutes to seconds, we multiply by 60. So, the Ferris wheel completes 3 revolutions every 2 minutes * 60 seconds = 120 seconds.
4. You notice that you are even with the center of the Ferris wheel, going down when the stopwatch is at 4 seconds.
Now, let's write the equation:
Let h(t) represent the height at a given time (t).
When the stopwatch reads 0 seconds, the height is the same as the center's height, which is 28m.
As the Ferris wheel rotates clockwise, your height decreases as time increases. The time it takes for one complete revolution can be found by dividing the total time (120 seconds) by the number of revolutions (3). So, the time for one revolution is 120 seconds / 3 = 40 seconds.
Since you are even with the center and going down when the stopwatch is at 4 seconds, we need to find the number of complete revolutions and add a fraction of a revolution to calculate your height.
Since 4 seconds is less than the time for one complete revolution (40 seconds), we need to consider a fraction of a revolution. 4 seconds / 40 seconds = 0.1 of a revolution.
To calculate your height, we subtract the fraction of a revolution from the center's height: h(t) = 28m - 0.1 revolutions * 2πr
Substituting the value of r (25m) into the equation, we have: h(t) = 28m - 0.1 revolutions * 2π * 25m
Simplifying the equation, we have:
h(t) = 28m - 0.1 * 2 * π * 25m
h(t) = 28m - 0.1 * 2 * 3.14 * 25m
h(t) = 28m - 0.1 * 6.28 * 25m
The final equation that expresses your height as a function of elapsed time is: h(t) = 28m - 15.7m * t
Therefore, your height (h) in meters can be calculated by subtracting 15.7m multiplied by the elapsed time (t) from the center's height (28m).