Shirley is on a Ferris wheel which spins at the rate of 3.2 revolutions per minute. The wheel has a radius of 35 feet, and the center of the wheel is 49 feet above the ground. After the wheel starts moving, Shirley takes 14 seconds to reach the top of the wheel.How high above the ground is she when the wheel has been moving for 6 minutes? (Round your answer to two decimal places.)
1) Center of the wheel is 49 feet above the ground that means top of the wheel is 98 feet above the ground 2) in 6 minutes the wheel would have revolved 6 times 3.2 revolutions that is 19.2 revolutions 3) a (0.2 revolution is an angle of 360*0.2 72 degrees (Or 0.4 Pi() ) The elevation of Shirley will be 35 sin ( 0.4Pi() ) 33.29 feet
The bottom of the Ferris wheel is 14 feet above the ground. The diameter of the wheel is 70 feet. Therefore, the maximum height of a person riding the wheel is 84 feet, and the minimum is 14 feet. The period is 18.75 seconds (this comes from 60 seconds / 3.2 revolutions) In the equation y AcosB(t-c) + D, the value of B 2π/period 8π/75 Also in this equation, A (Max ht. - Min ht.)/2 70/2 35 D (Max ht. + Min ht.)/2 98/2 49 Shirley's position above the ground after t seconds can be modeled by the equation: y(t) 35cos(8π/75)(t-14) + 49 After t 6 minutes 360 seconds: y(360) 35cos(8π/75)(360-14) + 49 35cos(2768π/75) + 49 15.49 ft.
