Question

The Ferris Wheel has a diameter of 30 meters, the center is 19 meters off the ground and it makes 2 revolutions per min.

Answer 1

The sinusoidal function for the height as a function of time will be h= -15 cos (πt/15)+19 meter

As the Ferris wheel starts with the rider from the bottom position (which is the minimum point in the cycle), we can represent the position of the rider with a negative cosine function.

The general form of the cosine function representing the displacement of the rider is:

f(t) = a cos(bt+c) + d, where:

amplitude = |a| which is the distance that travels above and below the midpoint

period = 2 π/|b| which is the time period i.e. time required to complete one cycle

-c/b is the phase shift.

d = vertical displacement of the function

Given the diameter of the wheel is 30 m, then r = 30/2 = 15 m.

So the distance that travels above and below the midpoint is the radius for which a=15. As we have the negative cosine function, a = -15.

The time period is 0.5min. As it is given the frequency is 2 revolutions per min for which b= 2(2π) rad/min.= 4π/60 rad/sec.= π/15 rad/sec.

The rider starts from the bottom position, so there will be no phase shift, so c=0

Given that the center of the wheel is 19 m above the ground, so d=19m

Therefore the equation will be

height of rider as function of time(t) = h = -15 cos (πt/15)+19 meter

Learn more about Sinusoidal function

here: brainly.com/question/2410297

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