MATH 1300 Study Guide - Quiz Guide: Ferris Wheel, 3E
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MATH 1300 Full Course Notes
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A ferris wheel with a radius of 10 meters is rotating at a rate of one revolution every two minutes. How fast is a rider rising when his seat is 16 meters above the ground? (assume the bottom of the ferris wheel is at ground level. Use the picture below or draw your own. ) [fyi: this is problem 4. 1. 40 of the text. ] With h and as in the picture, we know that (because the wheel goes around once=2 every two minutes) and we want to nd d dt. 2 radians minute (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)h=6 meters dh dt how fast the height is increasing when the rider is 16 meters o the ground (i. e. when h = 16 10 = 6). The quantities and h are related by. Di erentiating with respect to time, using the chain rule because both h and are functions of time, we get. When the rider is 16 meters above the ground, h = 6 and.
