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=(2\pi)/(40)* t\rightarrow x=(\pi)/(20)* 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 ((\pi)/(20)* t)\rightarrow height=-12\cos ((\pi)/(20)* t)\text{ + 17}`