Question

Which sinusoid all function gives the height of the rider

Answer 1

First, lets find an expression for the angle on the whell:

Lets say the 'x' is the angle that our passanger have in a given time. We know that in 40 seconds our passanger travels an angle of:

$2\pi$

So, using the rule of three, we can find that in 't' seconds he has an angle of:

$x=\frac{2\pi}{40}\times t\rightarrow x=\frac{\pi}{20}\times t$

now, lets draw again:

So, we can see that the height will be:

$\text{height}=5+(12-12\cos (x))\rightarrow height=17-12\cos (x)$

But we know the expression for the angle x, so:

$\text{height}=17-12\cos (\frac{\pi}{20}\times t)\rightarrow height=-12\cos (\frac{\pi}{20}\times t)\text{ + 17}$