Periodic Modeling Worksheets Grade 11

1. A Ferris wheel with a diameter of 40 meters completes one full revolution every 2 minutes. The boarding platform is 2 meters above ground level, and passengers board at the lowest point of the wheel. Liam boards the Ferris wheel at time t=0. Write a trigonometric function h(t) that models Liam's height above ground (in meters) as a function of time (in minutes).
2. A Ferris wheel has a maximum height of 61 meters and a minimum height of 16 meters. It completes one full revolution every 21 minutes. If Sophia boards the Ferris wheel at its lowest point, write the trigonometric function for her height h (in meters) after t minutes.
3. A buoy bobs up and down in the ocean as waves pass. Its vertical displacement (in meters) above its resting position can be modeled by a sinusoidal function. The buoy reaches a maximum height of 1.6 meters above its resting position and a minimum height of 1.6 meters below its resting position. It completes one full up-and-down cycle every 6 seconds. At t = 0 seconds, the buoy is at its resting position and moving upward. Write a sine function of the form y = A sin(Bx + C) + D that models the buoy's displacement y (in meters) at time t (in seconds). Then, determine the buoy's displacement after 1 second, rounded to the nearest tenth of a meter.

…and 3 more problems

1. A Ferris wheel with a diameter of 40 meters completes one full revolution every 2 minutes. The boarding platform is 2 meters above ground level, and passengers board at the lowest point. Liam boards the Ferris wheel at time t=0. Write a trigonometric function h(t) that models Liam's height above ground in meters as a function of time in minutes.
2. Emma is tracking the height of a Ferris wheel seat. The maximum height is 75 meters, the minimum height is 15 meters, and it completes one full revolution every 18 minutes. If the seat starts at its minimum height, write the trigonometric function for the height h(t) in meters after t minutes.
3. Hana is watching a buoy that bobs up and down with the waves. The buoy reaches a maximum height of 15 meters above the sea floor and a minimum height of 3 meters above the sea floor. It takes 18 seconds for the buoy to go from its highest point to its lowest point and back up to its highest point again. At time t = 0 seconds, the buoy is at its highest point. Write a sine function of the form h(t) = A sin(Bt + C) + D that models the height of the buoy above the sea floor in meters as a function of time t in seconds, and then use your model to find the height of the buoy exactly 33 seconds after it starts.

…and 3 more problems

1. sin(π/6) + cos(π/3) = ?
2. A vertical pole casts a shadow on horizontal ground. When the angle of elevation of the sun is 30°, the shadow is 12 meters long. Later in the day, when the angle of elevation is 60°, what is the length of the shadow?
3. Aroha is tracking the height of a Ferris wheel seat. The maximum height is 42 meters, minimum height is 10 meters, and it completes one revolution every 18 minutes. If the seat starts at its minimum height, write the trigonometric function h(t) = A sin(Bt + C) + D that models the height over time.

…and 5 more problems