## Answers

I don't think this is a cycloid

because i'm only in grade 11 math and have never heard that term before

this is from the "periodic function and their properties" unit

so, is it possible to give me an answer related to that?

thank you.

Thank you so much!.

You are dealing with a cycloid

A good start is Wikepedia, which has a nice illustration of the movement of the stone

http://en.wikipedia.org/wiki/Cycloid

Wolfram also has a good graphic.

http://mathworld.wolfram.com/Cycloid.html

they both show the equation.

careful, you have km/h and then cm and seconds, so you will have to conversions to do.

Well, it did ask you to draw the graph, and for that you can follow the path shown in the links I gave you.

For the period we simply have to know how long it takes for the wheel to make one rotation, that is, how long it takes for the stone to go from ground-level to ground-level.

The diameter of the wheel is 64π cm

it moves at 21.6 km/h

= 2160000/3600 cm/s

= 600 cm/s

since time = distance / rate

time to go 64π

= 64π/600 seconds

= .335 seconds

So roughly every 1/3 second it would complete what looks like a halfcircle.

since 2sec / .335 = appr 5.97

for a 2 second stretch of time, I would draw 6 of those loops.

for the first loop,

at t = 0, height = 0

at t = .335(1/4) , height = 32 , 1 quarter of rotation

at t = .335/2, height = 64 , half a rotation

at t = .335(3/4) , height = 32 , three-quarters of a rotation

at t = .335 , h = 0 , full rotation

draw a smooth curve to join the points.

etc..