Question

A Ferris wheel 50ft in diameter makes one revolution every 40sec. If the center of the wheel is 30ft above the ground, how long after reaching the low point is a rider 50ft above the ground?

Answer 1

I found: `15.91s` BUT check my maths....

Explanation:

Consider the (confused) diagram:

We can evaluate the angle `alpha` using trigonometry applied to the orange small triangle with height: `50-30=20"ft"` and hipotenuse equal to the radius `r=25"ft"`
so:
`20=25sin(alpha)`
`alpha=arcsin(20/25)=53.13^@`
So `50"ft"` of height corresponds to the total angle: `90^@+53.13^@=143.13^@=2.498"rad"`

Now:

Angular velocity is `omega=(2pi)/T=(2pi)/40=0.157"rad/s"`
To describe `2.498"rad"` it will take:
`t=2.498/0.157=15.91s`