Sine and Cosine 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.

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. Which other equations would model the graph 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 high above the ground is the CENTER of the ferris wheel?

(a)  

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)  

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)  

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)  

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)  

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)?

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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What will a person on this Ferris wheel be doing 67 seconds into their ride?

• Increasing at an increasing rate.

• Increasing at a decreasing rate.

• Decreasing at a decreasing rate.

• Decreasing at an increasing rate.

Answer explanation

Every 8 seconds is a cycle. So, at 64 seconds, the Ferris wheel starts a new cycle. The rider reaches their highest at 68 seconds. So, at 67 seconds, the graph is increasing and concave down (decreasing rate).