Ferris Wheel Trigonometry

A Ferris wheel with a 48-foot diameter makes one revolution every 3 minutes. The center of the wheel is 28 feet above the ground. A person on the Ferris wheel is closest to the ground at t=0 seconds. Let y=f(t) be the person's height above the ground at time t seconds.

At t=90 seconds, the person is at (a)   ft

A Ferris wheel with a 48-foot diameter makes one revolution every 3 minutes. The center of the wheel is 28 feet above the ground. A person on the Ferris wheel is closest to the ground at t=0 seconds. Let y=f(t) be the person's height above the ground at time t seconds.

At t=135 seconds, the person is at (a)   ft

A Ferris wheel with a 48-foot diameter makes one revolution every 3 minutes. The center of the wheel is 28 feet above the ground. A person on the Ferris wheel is closest to the ground at t=0 seconds. Let y=f(t) be the person's height above the ground at time t seconds.

At t=180 seconds, the person is at (a)   ft

If the Ferris wheel is placed on a stand 2 m higher lifting it further from the ground, and no other changes are made, the equation

y = asin[b(x +c)]+d

would be changed by

• increasing the amplitude of the graph by 2

• increasing the period of the graph by 2

• shifting the graph 2 units right

• shifting the midline 2 units up

Tags

CCSS.HSF-IF.C.7E

A Ferris wheel with a 48-foot diameter makes one revolution every 3 minutes. The center of the wheel is 28 feet above the ground. A person on the Ferris wheel is closest to the ground at t=0 seconds. Let y=f(t) be the person's height above the ground at time t seconds.

The amplitude of the Ferris wheel is (a)   ft

A Ferris wheel with a 48-foot diameter makes one revolution every 3 minutes. The center of the wheel is 28 feet above the ground. A person on the Ferris wheel is closest to the ground at t=0 seconds. Let y=f(t) be the person's height above the ground at time t seconds.

The period of the Ferris wheel is (a)   sec

A Ferris wheel with a 48-foot diameter makes one revolution every 3 minutes. The center of the wheel is 28 feet above the ground. A person on the Ferris wheel is closest to the ground at t=0 seconds. Let y=f(t) be the person's height above the ground at time t seconds. The equation of the Ferris wheel is y=-A\cos\left(\frac{\pi}{90}t\pi\right)+28. What is the value of A?

• 4

• 52

• 24

• 48

A Ferris wheel has a diameter of 38 ft. The bottom of the Ferris wheel is 3 ft. off the ground and it makes one revolution every 30 seconds. After you board the Ferris wheel it takes you 14 seconds to get to the top. Which function could represent your height off the ground as a function of time (in seconds) as you ride the Ferris wheel?

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).