EXAMPLE 2 Suppose you ride a Ferris wheel. The lowest point of the wheel is 3 meters off the ground, and its diameter is 20 m. After it started, the Ferris wheel revolves at a constant speed, and it takes 32 seconds to bring you back again to the riding point. After riding for 150 seconds, find your approximate height above the ground. .- EXAMPLE 2 We ignore first the fixed value of 3 m off the ground, and assume that the central position passes through the center of the wheel and is parallel to the ground. Let t be the time (in seconds) elapsed that you have been riding the Ferris wheel, and Y is he directed distance of your location with respect to the assumed central position at time t. Because '9' = #10 when t = 0, the appropriate model is v = --10 cos bt fort 2 0. 0 EXAMPLE 2 v = 10 cos ht for t 2 0. Given that the Ferris wheel takes 32 seconds to move from the lowest point to the next, the period is 32. ZF 32 b 1 If) m :9 z) " z ' - b 16 i \"I\" 16 Bringing back the original condition given in the problem that the riding point is 3 m off the ground, after riding for t = 150 seconds. 10 1501! + 13 y ms 16 1" it]. Hint You are approximatelv loCated 16.83 m off the ground. . EXAMPLE 1 A weight is suspended from a spring and is moving up and down in a simple harmonic motion. At start, the weight is pulled down 5 cm below the resting position, and then released. After 8 seconds, the weight reaches its highest location for the first time. Find the equation of the motion. 0 EXAMPLE 1 We are given that the weight is located at its lowest position at t = 0; that is, a = 5 (below the resting point). Therefore, the equation is y = -5 cos bt (cosine since the starting point is below the resting point) Because it took the weight 8 seconds from the lowest point to its immediate highest point, half the period is 8 seconds. 271 8 b it r 711 -= z) =:) 2 2 IN 8 y JCOSB Q SEHTWORK l. A weight is suspended from a spring and is moving up and down in a simple harmonic motion. At start, the weight is pushed up 6 cm above the resting position, and then released. After 14 seconds, the weight reaches again to its highest position. Find the equation of the motion, and locate the weight with respect to the resting position after 20 seconds since it was released. 2. Suppose the lowest point of a Ferris wheel is 1.5 meters off the ground, and its radius is 15 m. It makes one complete revolution every 30 seconds. Starting at the lowest point, find a cosine function that gives the height above the ground of a riding child in terms of the time t in seconds. 0