SOLUTION: Help please I have been trying to figure this out most of the day A person bungee cord jumping oscillates up and down. The distance from their highest point to their lowest poin

Question 1133032: Help please I have been trying to figure this out most of the day
A person bungee cord jumping oscillates up and down. The distance from their highest point to their lowest point is 10m. and the person takes 7 s to complete 2 cycles. For the first few cycles the distance from the mean position, d metres, with respect to t seconds, is modelled by a cosine function.
A)Sketch a graph of this function for two cycles.
B) Write an equation that describes the distance of the person from their mean position as a function of time.
c) at what height is the person after 9 seconds?
Thank you!!!!

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe the following graph models what you are looking for.

the equation is y = 5 * cos ( 72 /.7 * x)

the bungee cord starts at 5 meters above the mean position and drops to 5 meters below the mean position and ten back up to 5 meters above the mean position.

that's one full cycle.

it does this two times for two full cycles.

to model as 7 seconds for two full cycles, model as 3.5 seconds for one full cycle.

make the period of one full cycle equal to 3.5 degrees rather than 360 degrees.

the general formula of the cosine function is y = a * cos (b * (x - c)) + d

a is the amplitude.
b is the frequency
c is the horizontal displacement.
d is the vertical displacement.

the horizontal displacmeent will be 0 and the vertical displacement will be 0, so the formula becomes y = a * cos (b * x)

you want the cycle to peak at 5 units above the mean of 0 and bottom at 5 units beloe the mean of 0.

that makes the amplitude equal to 5.

the formula becomes y = 5 * cos (b * x).

your want the period to be 3.5 rather than 360.

period = 360 / frequency and frequency = 360 / period.

if the period is going to be 3.5, then frequency = 360 / period applies.

it becomes frequency = 360 / 3.5 which can also be shown as 720 / 7 if you just want to deal with integers.

the graph of the function of y = 5 * cos (720 / 7 * x) is shown below.

$$$

after 9 seconds, the person will be at y = 5 * cos (720 / 7 * 9) = 4.505 meters below the center line, which is what i think they mean by the mean.

this can be seen visually in the following graph.

$$$

the graph shows 3 full cycles of the cosine wave.

the first cycle ends at 3.5 seconds.
the second cycle ends at 7 seconds.
the third cycle ends at 10.5 seconds.

9 seconds is just a little past the midpoint of the third cycle.

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