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Write a general formula for finding the height of the rider during this time interval in the form of a sinusoidal function: h(t) = A sin(Bt-C) + D

Write a general formula for finding the height of the rider during this time interval in the form of a sinusoidal function: h(t) = A sin(Bt-C) + D

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter75: Drilling And Boring Compound-angular Holes
Section: Chapter Questions
Problem 13A
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macy Hufford More Ferris Wheel In the previous Ferris Wheel activity, you found Carlos's height at different positions on the Ferris wheel using right 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 E 30 F 15.3 G 612 Elapsed time since passing position A 1 second 2 seconds 3 seconds с 1. Calculate the height of a rider at each of the following times t, where t represents the number of seconds since the rider passed position A on the diagram. Keep track of any regularities you notice in the ways you calculate the height. As you calculate each height, plot the position on the Ferris wheel provided. 8 seconds 844.7 h(t)=25sin (18t)+30=441 (25Ft-Sin 36)+30 = 44.6946 25 sin(36) A 300, 20 14.5 seconds. J15.3 6.2 Height of the Rider Sin19=X+30 25 37.7 25936+30 44.7 6 seconds 259in72+ 30 53.7764 7.5 seconds 44.7 Sin54 +30 502 25 25 sin36+30 44.6946 Elapsed time since passing position A 5. sin(21) = cos(t) 18 seconds 23 seconds 28 seconds 36 seconds 40 seconds Height of the rider -25 Sin 36+30 = 15.3054 25 Sin36 +30= 44.6946 -25 Sin 72+30 =6.2236 30
Transcribed Image Text:macy Hufford More Ferris Wheel In the previous Ferris Wheel activity, you found Carlos's height at different positions on the Ferris wheel using right 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 E 30 F 15.3 G 612 Elapsed time since passing position A 1 second 2 seconds 3 seconds с 1. Calculate the height of a rider at each of the following times t, where t represents the number of seconds since the rider passed position A on the diagram. Keep track of any regularities you notice in the ways you calculate the height. As you calculate each height, plot the position on the Ferris wheel provided. 8 seconds 844.7 h(t)=25sin (18t)+30=441 (25Ft-Sin 36)+30 = 44.6946 25 sin(36) A 300, 20 14.5 seconds. J15.3 6.2 Height of the Rider Sin19=X+30 25 37.7 25936+30 44.7 6 seconds 259in72+ 30 53.7764 7.5 seconds 44.7 Sin54 +30 502 25 25 sin36+30 44.6946 Elapsed time since passing position A 5. sin(21) = cos(t) 18 seconds 23 seconds 28 seconds 36 seconds 40 seconds Height of the rider -25 Sin 36+30 = 15.3054 25 Sin36 +30= 44.6946 -25 Sin 72+30 =6.2236 30
4. 3. 2. Draw a graph of the height of the rider with respect to the elapsed time since passing position A Find the properties of the sinusoidal graph above: Amplitude, A = Midline, D = Period, P = Phase shift C/B = value of B = value of C = t Write a general formula for finding the height of the rider during this time interval in the form of a sinusoidal function: h(t) = A sin(Bt-C) + D
Transcribed Image Text:4. 3. 2. Draw a graph of the height of the rider with respect to the elapsed time since passing position A Find the properties of the sinusoidal graph above: Amplitude, A = Midline, D = Period, P = Phase shift C/B = value of B = value of C = t Write a general formula for finding the height of the rider during this time interval in the form of a sinusoidal function: h(t) = A sin(Bt-C) + D
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