Related rates with circular motion

[Dougggggg]

Homework Statement

I was really struggling with a Calculus problem but I think I have the right answer, this is more just checking with someone than anything.

When given a Ferris Wheel has a radius of 10 m, and that it takes 2 minutes for one rotation, find how fast it is moving from the ground 16 m up.

Homework Equations

x²+y² = r²

The Attempt at a Solution

I began by taking the derivative of the equation of a circle.

2x $$\frac{dx}{dt}$$ + 2y $$\frac{dy}{dt}$$ = 0

sin


Then used some trig to solve for $$\frac{dx}{dt}$$


cos$$\theta$$ = $$\frac{1}{r}$$x


I made a triangle with my x and y values in respect to the center of the Ferris Wheel. I also then need to account for my y value being from there and not the ground, so I now use 6 m.

-sin$$\theta$$ $$\frac{d\theta}{dt}$$ = $$\frac{1}{r}$$$$\frac{dx}{dt}$$

-rsin$$\theta$$$$\frac{d\theta}{dt}$$ = $$\frac{dx}{dt}$$


Also, could find $$\frac{d\theta}{dt}$$ = $$\pi$$

Finally solved for $$\frac{dy}{dt}$$


x($$\pi$$rsin$$\theta$$)=y$$\frac{dy}{dt}$$

$$\frac{dy}{dt}$$=8$$\pi$$


Yes, no, maybe so?

 

[mighty2000]

It looks like you are on the right track with your solution. However, I would suggest double checking your calculations and units to make sure they are correct. It's always a good idea to go through your solution step by step to ensure accuracy. It's also helpful to include units in your final answer. Overall, your approach seems sound and I believe you are on the right track. Keep up the good work!