Ferris Wheel Starter (Trig)

A person goes for a ride on a Ferris wheel. They enter one of the cars AT THE LOWEST possible point on the wheel from a platform 7 ft off the ground. When they are at the very top of the wheel, they are 92 feet off the ground. Let h represent the height of the car (in feet) and d the distance the car has traveled along the wheel's circumference from its starting location at the bottom of the wheel. We'll use the notation h=f(d), meaning height is a function of distance traveled.

How high above the ground is the CENTER of the ferris wheel?

A person goes for a ride on a Ferris wheel. They enter one of the cars AT THE LOWEST possible point on the wheel from a platform 7 ft off the ground. When they are at the very top of the wheel, they are 92 feet off the ground. Let h represent the height of the car (in feet) and d the distance the car has traveled along the wheel's circumference from its starting location at the bottom of the wheel. We'll use the notation h=f(d), meaning height is a function of distance traveled.

How far does the car travel in one complete trip around the wheel? (Round to the nearest whole foot!)

A person goes for a ride on a Ferris wheel. They enter one of the cars AT THE LOWEST possible point on the wheel from a platform 7 ft off the ground. When they are at the very top of the wheel, they are 92 feet off the ground. Let h represent the height of the car (in feet) and d the distance the car has traveled along the wheel's circumference from its starting location at the bottom of the wheel. We'll use the notation h=f(d), meaning height is a function of distance traveled.

What is the amplitude?

A person goes for a ride on a Ferris wheel. They enter one of the cars AT THE LOWEST possible point on the wheel from a platform 7 ft off the ground. When they are at the very top of the wheel, they are 92 feet off the ground. Let h represent the height of the car (in feet) and d the distance the car has traveled along the wheel's circumference from its starting location at the bottom of the wheel. We'll use the notation h=f(d), meaning height is a function of distance traveled.

What is the midline?

A person goes for a ride on a Ferris wheel. They enter one of the cars AT THE LOWEST possible point on the wheel from a platform 7 ft off the ground. When they are at the very top of the wheel, they are 92 feet off the ground. Let h represent the height of the car (in feet) and d the distance the car has traveled along the wheel's circumference from its starting location at the bottom of the wheel. We'll use the notation h=f(d), meaning height is a function of distance traveled.

What is the period? (How many feet does the Ferris wheel travel before it gets back to where it started? Round to the nearest whole foot!)

A person goes for a ride on a Ferris wheel. They enter one of the cars AT THE LOWEST possible point on the wheel from a platform 7 ft off the ground. When they are at the very top of the wheel, they are 92 feet off the ground. Let h represent the height of the car (in feet) and d the distance the car has traveled along the wheel's circumference from its starting location at the bottom of the wheel. We'll use the notation h=f(d), meaning height is a function of distance traveled.

If we want NO PHASE SHIFT, what function should I use?

• sine

• -sine

• -cosine

• cosine

A person goes for a ride on a Ferris wheel. They enter one of the cars AT THE LOWEST possible point on the wheel from a platform 7 ft off the ground. When they are at the very top of the wheel, they are 92 feet off the ground. Let h represent the height of the car (in feet) and d the distance the car has traveled along the wheel's circumference from its starting location at the bottom of the wheel. We'll use the notation h=f(d), meaning height is a function of distance traveled.

What is the correct equation for f(d)?

• $f\left(d\right)=-42.5\cos\left(267x\right)+49.5$

• $f\left(d\right)=-49.5\cos\left(\frac{2\pi}{267}x\right)+42.5$

• $f\left(d\right)=-42.5\cos\left(\frac{2\pi}{267}x\right)+49.5$

• $f\left(d\right)=-85\cos\left(\frac{2\pi}{267}x\right)+42.5$

A person goes for a ride on a Ferris wheel. They enter one of the cars AT THE LOWEST possible point on the wheel from a platform 7 ft off the ground. When they are at the very top of the wheel, they are 92 feet off the ground. Let h represent the height of the car (in feet) and d the distance the car has traveled along the wheel's circumference from its starting location at the bottom of the wheel. We'll use the notation h=f(d), meaning height is a function of distance traveled.

What is the correct graph for f(d)?

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A person goes for a ride on a Ferris wheel. They enter one of the cars AT THE LOWEST possible point on the wheel from a platform 7 ft off the ground. When they are at the very top of the wheel, they are 92 feet off the ground. Let h represent the height of the car (in feet) and d the distance the car has traveled along the wheel's circumference from its starting location at the bottom of the wheel. We'll use the notation h=f(d), meaning height is a function of distance traveled.

Which other equations would model the graph of the Ferris wheel?

•  $y=42.5\cos\left(\frac{2\pi}{267}\left(x-133.5\right)\right)+49.5$  

•  $y=42.5\sin\left(\frac{2\pi}{267}\left(x-133.5\right)\right)+49.5$  

•  $y=42.5\cos\left(\frac{2\pi}{267}\left(x-200.25\right)\right)+49.5$  

•  $y=42.5\sin\left(\frac{2\pi}{267}\left(x-66.75\right)\right)+49.5$