A ferris wheel has radius of 25 m and its centre is 27 m above the ground. It rotates once every 40 seconds. Sandy gets on the ferris wheel at its lowest point and the wheel starts to rotate.
Determine a sinusodial equation that gives her height, h, above the ground as a function of the elapsed time, t, where h is in metres and t in seconds. at what time is she 35m above the ground
To determine the sinusoidal equation for Sandy's height above the ground as a function of time, we can use the formula:
h(t) = A sin (B(t - C)) + D
where:
A = amplitude of the sinusoidal function (radius of the ferris wheel) = 25
B = vertical stretch factor = 2π / T, where T is the period of rotation = 40s
C = horizontal shift (phase shift) = 0, as she starts at the lowest point
D = vertical shift = 27
Therefore, the equation becomes:
h(t) = 25 sin ((2π / 40) t) + 27
h(t) = 25 sin (π/20) t + 27
To find out at what time Sandy is 35m above the ground, we can set h(t) = 35 and solve for t:
35 = 25 sin (π/20) t + 27
8 = 25 sin (π/20) t
sin (π/20) t = 8/25
t = arcsin (8/25) * 20 / π
t ≈ 13.49 seconds
Therefore, Sandy is 35m above the ground at approximately 13.49 seconds after she gets on the ferris wheel.