Thread: Related Rates Ferris Wheel Camera

Hello,
I am really stuck on a first year calculus related rates word problem involving a ferris wheel and a mounted camera. I am not sure where to start, so any help would be greatly appreciated. Thank-you.

Here is the question:

The third design question involves our plan to provide interested tourists with a video of themselves on our biggest Ferris wheel. The idea is to place a camera on a platform facing the descending seats. The camera will have to tilt at a rate that will enable it to keep the paying tourist in focus. The wheel is 60 metres in diameter with its lowest point 3 metres from the ground; takes about 20 minutes to make one revolution. Our plan is to mount the camera 15 metres from the ground, at a distance of 40 metres from the base of the ride. For how long will the camera be able to keep an individual in view and how fast must the camera rotate in order to do so? If you do not find our plan reasonable, please recommend a better one.

Basically, we have to solve the following question using first-year calculus, and then present our findings in a form that anyone can read and understand.

Originally Posted by rockafella

word problem

... more what I'd call a 'project', judging by

Originally Posted by rockafella

Basically, we have to solve the following question using first-year calculus, and then present our findings in a form that anyone can read and understand.

... and a lovely one, in which all your initial efforts drawing a meaningful sketch of the physical situatation...

Originally Posted by rockafella

I am not sure where to start

are used again for final presentation.

Your goal in the sketch is to explore geometry that could enable you to get, say, w, the angle of elevation of the camera from the horizontal, as a function of (result of doing math stuff to) theta, the angle of the customer's ferris wheel radius from the vertical ferris wheel radius. Then use the chain rule to relate the rates of the variables with respect to time...



... where



... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to t, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

Spoiler:

By all means come back for help with the geometry, showing what you've done and where you're stuck.

Good luck!

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