Trig Ferris wheel

Question

A Ferris wheel with a diameter of 10m rotates every 240 seconds. At time t=0 a rider is at the lowest height. 1.5m above ground. Determine a negative sine equation that gives h of rider above ground as a function of the elapsed time t where he is in meters and t is in seconds

Answer 1

It's important to remember what A, B, C, and D do in the sin equation Asin( Bx + C) + D

We need to find the values for A, B, C, and D and plug them in.

A is the amplitude which is the distance from the center of the graph. Since the diameter of the ferris wheel is 10m our sin graph must go up 5m and down 5m, in other words our amplitude is 5m, A = 5.

B determines the length of the period P or how long it takes to rotate. We use the following equation to find B or P depending on what we are looking for, in this case we need to find B. P = 2π/B

The problem states that P = 240, so using the equation I showed 240 = 2π/B

Multiply both sides by B to get 240B = 2π

Divide by 240 on both sides to get B = 2π/240

Simplify to get B = π/120

C is the horizontal shift but this problem didn't mention a horizonal shift so C = 0

D is the vertical shift. The ferris wheel being 1.5 meters above the ground gives us clue to find D but we also need to realize that a ferris wheel will be completely above ground and so the center of the ferris wheel is 5m (the amplitude) above the bottom of the ferris wheel. D = 5m +1.5m = 6.5 m

plugging in our values for A, B, C, and D and s the problem says to use h for height we have,

h = -5sin( πx/120 ) + 6.5

( I put the negative sign because the problem asks for the negative sine equation)