Question

You are standing at a base of a Ferris Wheel which is 4 m above ground while your friend is riding. The Ferris Wheel is 8m in diameter. Describe how the shape of the sine curve models the distance your friend is to the platform you are on. Identify the function that will model this situation as well as a function that will model the if we measure his distance to the ground. In your explanation use the following terms:

• Sine
• Function
• Radius
• Repeat
• Rotate
• Amplitude
• Period
• Intercept
• Maximum
• Minimum
• Axis of the curve

Answer 1

As the ferrie wheel rotates the distance of his friend increases from the platform in which he stands and the distance curve follows the trigonometric curve as sine or cosine function. If it follows the sine curve the vertical shift is 4m up and horizontal shift is (π/2)radian right. And the amplitude of this curve is equal to radius of the ferrie wheel. This curve repeats after each revolution or rotation of 2π radian. The period of this curve is depend on the angular velocity of the ferrie wheel, that is , if 'w' be the angular velocity of the ferrie wheel than time period is equal to (2π/w). The intercept of this curve is on the y axis says that at initial time the position of his friend from the base of the ferrie wheel, here i consider the initial position is at height zero from the platform. The maximum distance of his friend from the platform is when the ferrie wheel rotates π radian of angle or half rotation, which is equal to the diameter of the ferrie wheel from the base of it. And the minimum distance from base is zero. The axis of the curve is at a height of 4m from the base, and 8m from the ground.