1. a) A Ferris wheel of diameter 26 m takes 24 seconds to complete 3 rotations. If passengers board the lowest car at a height of 2 m above the ground, determine a sine function that models the height, h, in metres, of the car relative to the ground as a function of the time, t, in seconds. Include a sketch. b) Using your equation from part a), find the height after 1.25 seconds. c) Using your equation from part a), find how long it takes the passenger to reach a height of 18m in the first rotation.

1. a) A Ferris wheel of diameter 26 m takes 24 seconds to complete 3 rotations. If passengers board the lowest car at a height of 2 m above the ground, determine a sine function that models the height, h, in metres, of the car relative to the ground as a function of the time, t, in seconds. Include a sketch. b) Using your equation from part a), find the height after 1.25 seconds. c) Using your equation from part a), find how long it takes the passenger to reach a height of 18m in the first rotation.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Trigonometry

Section1.8: Applications And Models

Problem 4E: The number of cycles per second of a point in simple harmonic motion is its .

See similar textbooks

Similar questions

Al has a pet hamster, Fred, who he loves to run on his wheel. The hamster wheel has a diameter of 12 cm and the base of the wheel is 2 cm off the ground. Fred can turn the wheel 3 times each second. a) Starting from the lowest point, sketch three cycles of the function below. b) Write an equation (in terms of sine or cosine) to model Fred running on the hamster wheel. Use radian measure. c) Use the equation to determine the height of the wheel at 4.2 seconds. Use a radian measure and round your answer to the nearest tenth.
You play a carnival game, where toy ducks are floating in a wave pool. After 1 second, your duck is floating on the peak of a wave 8cm above the bottom of the pool. After 3 seconds, your duck is at the bottom of the wave 2cm from the bottom of the pool. Write an equation for sine and cosine that describes your duck’s motion.
A piano tuner uses a tuning fork. If middle C has a frequency of 264 vibrations per second, write an equation in the form d = sin ωt for the simple harmonic motion.
zit.com -serp-php 30. Use the function f (x ) A. Find the period. = 3sin(2x- TT) to answer the questions. B. Find the amplitude.
Suppose you take a ride on a Ferris Wheel that has a radius of 100 feet. The center of the wheel is 110 feet above the ground and it takes 20 minutes to make a complete revolution. You board in the 6:00 position. Write an equation for h(t), which models your height above the ground, in feet, as a function of the time t, in minutes, since you boarded the Ferris Wheel. Your equation should refer to radians, not to degrees. Indicate the amplitude, the period and the equation of the midline. 3.1 Equation: h(t) =, 3.2 Amplitude: 3.3 Period: 3.4 Midline: 3.5 Determine the angular speed of the Ferris wheel. Units should be degrees per minute. The angular speed is degrees per minute.
In whoville, the amount of rainfall varies greatly each week and follows a sinusoidal pattern. The following data is the recorded millimeters (mm) of precipitation across 14 weeks. Determine a sine and a cosine function that approximates the amount of rainfall over time in weeks. Decimals are allowed. Week 1, rainfall(mm) - 1.4 Week 2, rainfall(mm) - 3.1 Week 3, rainfall(mm) - 4.3 Week 4, rainfall(mm) - 2.9 Week 5, rainfall(mm) - 1.2 Week 6, rainfall(mm) - 0.1 Week 7, rainfall(mm) - 1.3 Week 8, rainfall(mm) - 2.7 Week 9, rainfall(mm) - 4.3 Week 10, rainfall(mm) - 3.2 Week 11, rainfall(mm) - 1.1 Week 12, rainfall(mm) - 0.2 Week 13, rainfall(mm) - 1.2 Week 14, rainfall(mm) - 2.8
A height of a rider on a Ferris wheel can be modeled using a sinusoidal function. The rider's height, h in meters, above ground vs time, t in seconds, can be described using the equation h = -16 cos(6t) + 18 11. a) Graph the rider's height above the ground during a 3-minute ride. b) Determine the height of the rider after 110 s. The Ferris Wheel 40 36 32 c) During the 3-minute ride, how long is the rider at or 28 above 26 m? 24 20 16 12 4. 30 60 90 120 150 180 Time (seconds)
A table fan has a mark on the tip of one blade. The equation >= 16 sin(4x) + 23 represents. the height of the mark, y centimetres, above the table x seconds after the fan is turned on. What is the distance from the mark to the tip of the opposite blade? Hint: If you draw a horizontal line through the center, from tip to tip, how long is the line?