Help please macy HuffordMore Ferris WheelIn the previous Ferris Wheel activity, you found Carlos's height at different positions on the Ferris wheel usingright triangles, as illustrated in the diagram.Recall the following facts from the previous lesson:The Ferris wheel has a radius of 25 feet.The center of the Ferris wheel is 30 feet above the ground.Carlos has also been carefully timing the rotation of the wheel and has observed the following additional fact:The Ferris wheel makes one complete revolution counterclockwise every 20 seconds.538 D..41.7 E30 F15.3 G612Elapsed timesince passingposition A1 second2 seconds3 secondsс1. Calculate the height of a rider at each of the following times t, where t represents the number ofseconds since the rider passed position A on the diagram. Keep track of any regularities you notice inthe ways you calculate the height. As you calculate each height, plot the position on the Ferris wheelprovided.8 seconds844.7 h(t)=25sin (18t)+30=441(25Ft-Sin 36)+30= 44.694625 sin(36)A 300, 2014.5 seconds.J15.36.2Height of theRiderSin19=X+302537.725936+3044.76 seconds 259in72+ 3053.77647.5 seconds 44.7Sin54 +30502 2525 sin36+3044.6946Elapsed time sincepassing position A5. sin(21) = cos(t)18 seconds23 seconds28 seconds36 seconds40 secondsHeight of the rider-25 Sin 36+30= 15.305425 Sin36 +30=44.6946-25 Sin 72+30=6.223630 4.3.2. Draw a graph of the height of the rider with respect to the elapsed time since passing position AFind the properties of the sinusoidal graph above:Amplitude, A =Midline, D =Period, P =Phase shift C/B =value of B =value of C =tWrite a general formula for finding the height of the rider during this time interval in the form of asinusoidal function:h(t) = A sin(Bt-C) + D

If the center of the Ferris wheel is above 30 feet from the ground and its radius is 25 feet that mean the height of the platform on which the Ferris wheel stands is 5 feet tall. R = 25 feet Speed of the rider = (circumference of the wheel) / (total time taken to complete the revolution) Speed of the rider = 2πR20 = 5π2ft/s If at any time 't' the rider is at a point 'B' and the angle AOB =θ. Then, The length of arc AB = Rθ = 25θ Length of the arc AB = Speed of the rider * t Therefore, 25θ = 5π2t θ = πt10 radian θ = 180 *t10 = 18t degrees cos(θ) = xRx = Rcos(θ)x = 25cos(πt10) = 25cos(18t) At the time 't', The height of the rider from the ground = 5 + R - x = 30 - x H = 30 - 25cos(18t)Part (1) time height time height 1s 30 - 25cos (18) = 6.22ft. 14.5s 30 - 25cos (261) = 33.9ft. 2s 30 - 25cos (36) = 9.77ft. 18s 30 - 25cos (324) = 9.77ft. 3s 30 - 25cos (54) = 15.305ft. 23s 30 - 25cos (414) = 15.305ft. 6s 30 - 25cos (108) = 37.72ft. 28s 30 - 25cos (504) = 50.225ft. 7.5s 30 - 25cos (135) = 47.67ft. 36s 30 - 25cos (648) = 22.27ft. 8s 30 - 25cos (144) = 50.22ft. 40s 30 - 25cos (720) = 5ft.Part (2) Since, the rider will repeat his/her all the positions after every revolution is completed which means after every 20 seconds, the rider will repeat his/her path. Therefore, the graph of the height of the rider will be periodic. The maximum height that can be attained by the rider = when the rider is at the top = 30 + 25 = 55feet The minimum height that can be attained by the rider = when he is at the starting position = 5feet So, the graph of the height of the rider with respect to time is,Part (3) H = 30 - 25cos(18t) cos (18t) = sin (90 - 18t) = -sin (18t - 90) H = 30 - 25sin (90 - 18t) H = 25sin (18t - 90) + 30 Therefore, Amplitude, A = 25 Midline, D = 30 Since the graph is repeating itself after every 20 seconds, therefore, Period, P = 20s Phase shift, C/B = 90/18 = 5 B = 18 C = 90 Part (4) sinusoidal function for the height of the rider at a time 't', h(t) = 25sin (18t - 90) + 30