At one time, Maple Leaf Village (which no longer exists) had North America’s largest Ferris wheel. The Ferris wheel had a diameter of 56 m, and one revolution took 2.5 min to complete. Riders could see Niagara Falls if they were higher than 50 m above the ground. Sketch three cycles of a graph that represents the height of a rider above the ground, as a function of time, if the rider gets on at a height of 0.5 m at t=0 min.Then determine the time intervals when the rider could see Niagara Falls
The first thing I will do is a sine curve. The period must be 2. 5 min, .... 2. 5 = 2π/k, k = 4π/5 so we start with sin 4πt/5 the amplitude must be 56 so ... 56 sin 4πt/5 The min is something we want to be. 0 so we have to raise it all up by 56.5 so far we have h = 56 sin 4πt/5 + 56.5 I am testing what I have so far. t = 0, h = 56.5 t is the same as t. 625, h = 112. 5 .. the max t = 1. 25 , h = 56.5 t = 1. 875 , h = . 5 .. the min but you wanted the min to be when t = 0, so I will shift the curve . 625 units to the right y = 56 sin 4π/5(t - . 625) + 56.5 when is h above 50 m ? 50 = 56 sin 4π/5(t - . 625) + 56.5 56 sin 4π/5(t - . 625) = -6.5 sin 4π/5(t - . 625) = -.11607 4π/5(t - . 625) = 3. 2579 or 6.16685 t-.625 = 1. 2963 or 2.4537 t = 1. 9213 or 3. 0787 minutes so the time interval where the person would be 50 m is 3. 0787 - 1. 9213 = 1. 157 minutes, and thus the time he would be above the 50 m is 2.5 - 1. 157 = 1. 343 minutes
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