Question

The diameter of a Ferris wheel is 10 meters. From a platform 2 meters above the ground, you board the Ferris wheel at the bottom. Determine an equation for a rider's height in relation to time if it takes 35 seconds to reach the summit. Sketch the graph.

Answer 1

Solution:

$d=10\ m \\ r=5\ m$

So, amplitude$=a=5$

It takes 35 seconds to reach the summit.

So, 70 seconds for one complete revolution.

$b=\dfrac{2\pi}{70}=\dfrac{\pi}{35}$

The lowest point is 2 m off the ground and the radius is 5 m, so the midline will be at 7 m.

Thus, equation is: $h(t)=-5\cos\dfrac{\pi}{35}t+7$

Assume it as $y=-5\cos\dfrac{\pi}{35}x+7$

Its graph is: