Let
t------> the time in seconds.
we know that
Since the wheel has a radius of 15 meters and the top of the wheel is 35 meters above the ground, the bottom of the wheel is 5 meters above the ground.
The height of the rider on the wheel is given by the function
h = 20 − 15 cos θ--------> equation 1
where
θ is the angle between the radius from the center of the wheel to its bottom and the radius from the center of the wheel to the rider's position.
Check
For θ = 0°
h = 20 − 15 cos 0°------ h=20-15=5 m
For θ = 90°
h = 20 − 15 cos 90°------ h=20 m
For θ = 180°
h = 20 − 15 cos 180°------ h=20+15=35 m
For θ = 270°
h = 20 − 15 cos 270°------ h=20 m
For θ = 360°
h = 20 − 15 cos 0°------ h=20-15=5 m
The next step is to write the angle in terms of time.
You were given the time for the wheel to rotate around once, 20 seconds. This means that it rotates one revolution every 20 seconds.
If you want the formula in terms of degrees, you would use the angular velocity
ω = 360°/20 s = 18°/s.
If you want the formula in terms of radians, however, where one rotation equals 2π radians.
In this case, the angular velocity is
ω = 2π/20 = π/10 rad/s.
Once you know ω,
you can find θ using the formula ω = θ/t.
So
θ = ωt = (π/10)t = πt/10.
Once you plug this into the equation 1 above, you will get
h = 20 - 15 cos (πt/10)
therefore
the answer is
h = 20 - 15 cos (πt/10)
