SOLUTION: Eric is riding a Ferris wheel. The wheel makes 1 revolution every 48 seconds. The wheel has a diameter of 60 feet. Eric stars the ride at the bottom, 3 feet above the ground. A)

Question 1141816: Eric is riding a Ferris wheel. The wheel makes 1 revolution every 48 seconds. The wheel has a diameter of 60 feet. Eric stars the ride at the bottom, 3 feet above the ground.
A) write down a function for Eric’s height after x seconds.
B) If the full ride last 4 minutes, how many times does it go around?
C) List all of the times that Eric is 18 feet above the ground.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the equation that i get is:

y = 30 * sine (7.5 * (x - 12)) + 33.

this is based on the general equation of y = a * sine (b * (x - c)) + d

a is the amplitude which is equal to plus or minus the distance from the center line of the sine wave.

since the diameter is 60, the radius is 30, and the amplitude is therefore 30.

b = the frequency.

the formula for frequency is f = 360 / p.

f is the frequency.
p is the period.

since the period is 48, the formula becomes f = 360 / 48 = 7.5.

what this says is there are 7.5 complete cycles of the sine wave in 360 degrees.

the formula for period is p = 360 / f.

360 / 7.5 = 48 for the period.

c = the horizontal shift.

since the sine wave normally starts at the center line, we need to shift the sine wave so that it starts at the bottom of the cycle.

if you graphed y = 30 * sine (7.5 * x), you would have seen that the sine wave hits bottom at -12 degrees.

we need to shift it to the right to that the value of the sine wave at 0 degrees is the same as the sine wave at - 12 degrees.

therefore, the value of c is equal to 12, and the formula becomes y = 30 * sine (7.5 * (x - 12)).

finally, the bottom of the sine wave needs to be 3 feet above the ground.

the ground is the x-axis, therefore d must be equal to 33, so that the bottom of the sine wave stops at 3 units above the x-axis.

the final equation is y = 30 * sine (7.5 * (x - 12)) + 33.

this is what the graph looks like.

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any questions, write to dtheophilis@gmail.com.

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