How would you do this problem? Suppose that after you are loaded into a Ferris wheel car, the wheel begins turning at 4 rpm. The wheel has diameter 12 m and the bottom seat of the wheel is 1 m above the ground. express the height h of the seat above the ground as a function of time t seconds after it begins turning.

Question

anonymous · Answer

This one is probably gonna be a sine/cos wave function, right? The cosine wave equation is
y=acos(b(x−c))+d
You're one meter of the ground, the height is always positive, and the highest point is 13 meters, so we need to take 1 + our amplitude, which is 12, so d = 7,  the amplitude is 6, meaning the derivation from zero, so a = -6. Now comes the tricky part, where we have to find b and c.  As far as we're concerned, the ride starts at 0 on the x axis, so we can say that c = 0. Now 
y=-6cos(b(x))+7
solvable with the given information. We know that every 15 seconds, one rotation happens.
A normal period can be shown by the equation$$b \times \left( x - c\right) = 2\pi$$
c is 0, so $$b \times 15 = 2\pi$$
$$b = \frac{ \pi }{ 15 }$$
The full equation is $$h = -6\cos(\frac{ 2\pi }{ 15 } \times t) + 7$$
... I think.

anonymous · Answer

thank you so much. this finally makes sense