Question

A ferris wheel is 24 meters in diameter and must be boarded from a platform that is 6 meters above the ground (as illustrated). Suppose the wheel turns in a counter-clockwise direction, you find that it take 2 minutes to reach the top, at 30 meters, and completes a full revolution every 4 minutes. Which equation accurately shows the distance to the ground in terms of time, x? y=24cos(4x)−30y is equal to 24 cosine 4 x minus 30 y=12cos[π2(x−2)]+18y is equal to 12 cosine open bracket pi over 2 times open paren x minus 2 close paren close bracket plus 18 y=12cos(π2x)+6y is equal to 12 cosine open paren pi over 2 x close paren plus 6 y=12cos[4(x−2)]+18y is equal to 12 cosine open bracket 4 times open paren x minus 2 close paren close bracket plus 18

Answer 1

The correct option is;

y = 12·cos[π/2·(x- 2)] + 18

Explanation:

The general equation for the motion of a Ferris wheel as a function of time, t, can be presented as follows;

f(t) = A·cos(B·x + C) + D

Where;

A = The amplitude = Diameter/2 = 24/2 = 12 meters

The period = 4 minutes

B = 2·π/Period = 2·π/4 = π/2

D = The midline = 6 + 12 = 18 meters

Substituting the values gives;

f(x) = 12·cos(π/2·x + C) + 18

At x = 0, we have

f(x) = 6 = 12·cos(π/2×0 + C) + 18

cos( C) = (6 - 18)/12 = -1

∴ C = -π

We therefore have;

f(t) = y = 12·cos(π/2·t - π) + 18 = 12·cos[π/2·(x- 2)] + 18

y = 12·cos[π/2·(x- 2)] + 18.