I have a trig question regarding a ferris wheel, radius 35m, axles 37m, clockwise direction, rotates twice every 10 mins. I have calculated the following function:
h = -35cos(2pi*X/5)+37
I have calculated at what height I would be after 3 minutes by substituting X=3 in the above equation. However, I need to calculate at what times I would be 30m off the ground. Can you please tell me if I am on the right track and how to calculate the time?
Many thanks
I agree with your equation, so let' set it equal to 30
30 = -35cos(2pi*X/5)+37
-7 = -35cos(2pi*X/5)
.2 = cos(2pi*X/5)
take the inverse cosine to get
2pi*X/5 = 1.369438
x = 1.09 minutes
check it by repeating the same steps you did finding the height at 3 minutes.
Many thanks, I understand that now.
I have another question I am stuck on also. How do I get an equation for the height of the car on the ferris wheel over a 10 minute period if we start the analysis one minute into the ride.
Can I still use the original formula
h = -35cos(2pi*X/5)+37
I don't understand what part changes to make it one minute into the ride. Appreciate any help.
Yes, you are on the right track with your equation. The equation you have, h = -35cos(2pi*X/5) + 37, represents the height (h) at a given time (X) on the ferris wheel.
To calculate at what times you would be 30m off the ground, you want to solve the equation for h = 30. So, you need to substitute h = 30 into the equation and solve for X.
Let's set up the equation:
30 = -35cos(2pi*X/5) + 37
To isolate the cosine term, you can move 37 to the right side:
30 - 37 = -35cos(2pi*X/5)
Simplifying further:
-7 = -35cos(2pi*X/5)
To get rid of the negative sign, you can multiply both sides by -1:
7 = 35cos(2pi*X/5)
Now divide both sides by 35:
7/35 = cos(2pi*X/5)
Simplify:
1/5 = cos(2pi*X/5)
This equation tells us that the cosine of a certain angle is equal to 1/5. To find the angle, you can use the inverse cosine or arccos function. In this case, arccos(1/5) represents the angle that has a cosine value of 1/5.
Using a calculator, you can find that arccos(1/5) is approximately 1.3694 radians (or about 78.68 degrees).
So, we have:
2pi*X/5 = 1.3694
Now, solve for X by dividing both sides by 2pi/5:
X = (1.3694 * 5) / (2pi)
Using a calculator, you can find the value of X to be approximately 1.097 minutes.
Therefore, you would be approximately 30m off the ground at around 1.097 minutes after starting the ride.
Remember to clarify the direction of rotation (clockwise in your case) when interpreting the results.