Question

Help please! it's a long question..
Aunt Norma is riding a Ferris wheel. The Ferris wheel has a radius of 50 feet, and the center of the wheel is 58 feet off the ground. The wheel is spinning counterclockwise with an angular velocity of 0.2 radians per second. Uncle Norm is standing in the plane of the Ferris wheel, 60 feet to the right of the base at a height of 0 feet.
a)How fast is the distance between Aunt Norma and the center of the wheel changing when she is 28 feet off the ground and going up?

Answer 1

\[x^2+y^2=50^2\]\[x=\pm\sqrt{50^2-y^2}\]Set \(y=28-58\) and profit! Is there a step you don't understand?

Answer 2

i dont quite understand why you used the pythagorium theorem. :/

Answer 3

That's the equation for a circle, believe it or not. :)

Answer 4

so y=28-58=-30ft
and then do I just plug it back into
\[\pm \sqrt{50^2-(-30)^2}\]

Answer 5

Nyess, then pick whichever \(x\) makes the most sense.

Answer 6

so then x=plus or minus 40
so that means tthe distance of aunt norma and the center of the wheel is changing at 40 ft/sec when she is 28 feet off the ground and moving up..?

Answer 7

I'm sorry, didn't read the question fully. XD Give me time to type out an actual answer.

Answer 8

Aunt Norma is riding the wheel. Therefore the radius stays fixed. :|

Answer 9

What I gave you the solution to earlier was the position, by the way. But the radius of the Ferris wheel is fixed.

Answer 10

ahaha oh. that's what i thought at first. thank you! i feel like i wasted your time :(
can I ask another question?

Answer 11

Yes.

Answer 12

okay.
How fast is the distance between Aunt Norma and Uncle Norm changing when she is 28 feet off the ground and going up?

Answer 13

This was the question I thought you were asking. XD Let's see if I can do this.

Answer 14

Alright, wait a sec, need paper and pencil lol.