trigonometry functions

Question

You and your best friend choose to ride the Capitol Wheel at the National Harbor. Your distance from the ground varies sinusoidally with the time since the wheel began to move.

1. Let t be the number of seconds that have elapsed since you started your ride on the ferris wheel.
2. You start at the lowest point of the wheel, 13 feet above the ground.
3. You find that the wheel makes 1 revolution every 40 seconds.
4. The diameter of the wheel is 60 feet.
5. Answers should include units & round to the nearest hundredths place

1. 1. What is the highest point the rider will ever reach above the ground?
2. 2. At what time will the rider be at the highest point?
3. 3. Write an equation describing the distance (d) the Ferris Wheel is above the ground with respect to time, L (in radians) Hint: Draw a graph to help write the equation.
4. 4. What is the location of the rider at time t=11 seconds?

Answer 1

1. 1. What is the highest point the rider will ever reach above the ground?

Starting height + tallest point on wheel = 13+60= 73ft

1. 2. At what time will the rider be at the highest point?

1 half revolution from ground gets you to the tallest point on the wheel.

1. 3. Write an equation describing the distance (d) the Ferris Wheel is above the ground with respect to time, L (in radians) Hint: Draw a graph to help write the equation.

T = 40, A = 60/2=30->use cosine -> cos(2pit/40)=cos(pi t/20)

d(t) = 30(1-cos(pi t/20)) + 13

1. 4. What is the location of the rider at time t=11 seconds?

plug in, should get arround 47.7ft.

This is a visual problem so I can't explain it very well in this format. Please feel free to reach out for online tutorials.

-Trent