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A carnival ferris wheel with a radius of 7m rotates once every 16 seconds. The bottom of the wheel is 1m above the ground.

Find the equation of the function that gives a rider's height above the ground in meters as a function of time, in seconds, with the rider starting at the bottom of the wheel.

Please use math tools to state your answer - see hint. Or attach your work as ONE easy to read file.

Respuesta :

oladayoademosu

The equation of the function that gives a rider's height above the ground in meters as a function of time, in seconds is y(t) = 14sin(πt/8) + 1

The equation of the function that gives the height of the ferris wheel

Since the motion of the ferris wheel is periodic,it follows a sinusoidal function form.

So, the general form of a sine function y(t) is

y(t) = Asin(2πt/T) + K where

  • A = amplitude,
  • T = period,
  • t = time and
  • K = vertical shift

Now since radius of 7m, the maximum value from its lowest point is at y = 2r + 1 = 2 × 7 + 1 = 14 + 1 = 15 at sin(2πt/T) = 1 which is the maximum value for sinФ = 1.

Since the bottom of the wheel is 1m above the ground, its minimum value is y = 1 at t = 0.

Also, it rotates once every 16 seconds, so its period T = 16 s.

So, y(t) = Asin(2πt/T) + K

y(t) = Asin(2πt/16) + K

y(t) = Asin(πt/8) + K

At maximum value

15 = Asin(πt/8) + K

15 = A + K  (1)

At minimum value

1 = Asin(πt/8) + K

1 = A(0) + K  

1 = 0 + K

K = 1

Substituting K into (1), we have

15 = A + 1

15 - 1 = A

14 = A

A = 14

So, y(t) = Asin(πt/8) + K

y(t) = 14sin(πt/8) + 1

So, the equation of the function that gives a rider's height above the ground in meters as a function of time, in seconds, with the rider starting at the bottom of the wheel is y(t) = 14sin(πt/8) + 1

Learn more about sine function here:

https://brainly.com/question/12595712

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