# What mistake did I make while solving the Ferris wheel trig problem?

• MHB
• NeedHelp27
In summary, the problem at hand is to determine how long after reaching the low point a rider on a Ferris wheel, with a diameter of 50 ft and a center 30 ft above the ground, will be 50 ft above the ground. The task is modeled using an equation, f(t)=-25cos((pi/20)t)+30, and the solution involves finding the point in time where the rider reaches the low point, t=0.
NeedHelp27
Hello, all. For homework, we got a problem that reads as follows: A Ferris wheel 50 ft in diameter makes one revolution every 40 sec. If the center of the wheel is 30 ft above the ground, how long after reaching the low point is a rider 50 ft above the ground? Our teacher said to model the situation with an equation.

When I tried to go about doing this, I drew a graph showing the person's height, at it ended up being the cosine graph shifted up 5 and over so that a low point was on the y-axis (0,5). Next, I tried to write the equation in the form f(x)=acos(bx+c)+d. I did (max value - min value)/2 = (55-5)/2=25 to find a. Then, because one revolution takes 40 seconds, I solved 2pi/b=40 for b and got b=pi/20. The graph is shifted 5 up, so d-5. That gave me f(x)=25cos((pix)/20+c)+5. I also have the point (0,5) on the graph, so I can plug it into get c. f(0)=5=25cos(c)+5. C ended up being pi/2.

Then I went to solve the problem.
f(t)=50=25cos((pix)/20+pi/2)+5.
When I finally isolated x, I got a domain error. Where did I go wrong?

If we let the point in time (in seconds) where the rider is at the lowest point be $t=0$, then we could write:

$$\displaystyle f(t)=-25\cos\left(\frac{\pi}{20}t\right)+30$$

Now try solving the question. :D

## 1. What is the "Ferris Wheel Trig Problem"?

The "Ferris Wheel Trig Problem" is a mathematical problem that involves using trigonometry to calculate the height of a rider on a Ferris wheel at a given time.

## 2. How is the "Ferris Wheel Trig Problem" solved?

The "Ferris Wheel Trig Problem" is solved using the trigonometric functions sine, cosine, and tangent. The specific function used depends on the given information and what the problem is asking to solve for.

## 3. What information is needed to solve the "Ferris Wheel Trig Problem"?

To solve the "Ferris Wheel Trig Problem", you need to know the radius of the Ferris wheel, the distance from the ground to the center of the wheel, and the time at which you want to calculate the height of the rider.

## 4. Can the "Ferris Wheel Trig Problem" be solved without using trigonometry?

No, the "Ferris Wheel Trig Problem" cannot be solved without using trigonometry. The problem involves calculating the height of a rider using the angles and distances involved in a rotating circle, which is where trigonometry is necessary.

## 5. How is the "Ferris Wheel Trig Problem" used in real life?

The "Ferris Wheel Trig Problem" is used in real life by engineers and designers when creating and testing Ferris wheels. It allows them to calculate the height of the riders at different points during the ride and make adjustments to ensure a safe and enjoyable experience. Trigonometry is also used in other fields such as navigation and astronomy.

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