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 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. 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).