Expert: Paul Klarreich - 10/12/2009

Question
Here's some background information for the problem:
 One day w decide to go to six flags. They decide to do the bungee jump. They start at a height of 80 feet. Once they have fallen, they gently swing back and forth, up and down (like a pendulum). The closest they get to the ground is 10 feet, they are furthest away from the ground at 25 feet, and it takes them 2 seconds to get from "up" to "down" and back to "up" again.
  
  A) make a table that compares the riders' height(from the ground) over time.
   ** How would u go about doing this? I tried splitting the times up by 2 sec's.; 0,2,4,6,8 for the x values as 8 being the period but I'm sure that's wrong. I don't know how to find the period from this.
  B) Write an equation for the function expressing the riders' height from the ground (h) as a function of time (t).
    I assume u have to find the amplitude, the period, and the mid line, and put it into the equation: y= a sin(bx)+d
but i don't know how to do this with the given information.
   
    *** I am having a lot of trouble with this and i would just like to thank you so much ahead of time for taking the time to help me with this problem.Thank you soo much!

Answer
Questioner: nicolette
Country: United States
Category: Calculus
Private: No
Subject: Pre Calculus- sine and cosine waves
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Hi, Nicolette,

Question: Here's some background information for the problem:
One day we decide to go to six flags. They decide to do the bungee jump.

>> I always like a nice story.  

They start at a height of 80 feet.

>> That seems irrelevant. (Put in to confuse you, I think.)

Once they have fallen, they gently swing back and forth, up and down (like a pendulum).

>> Which is it?  Back and forth like a pendulum, or up and down like a bungee?  I think you mean the second.

The closest they get to the ground is 10 feet, they are furthest away from the ground at 25 feet,

>> Ah! That looks like it's telling us the AMPLITUDE.  It would be half of the difference, or 7.5

and it takes them 2 seconds to get from "up" to "down" and back to "up" again.

>> and that looks like a period, as in sine-or-cosine(2 pi t/2 seconds)
 
A) make a table that compares the riders' height(from the ground) over time.
  ** How would u go about doing this? I tried splitting the times up by 2 sec's.; 0,2,4,6,8 for the x values as 8 being the period but I'm sure that's wrong. I don't know how to find the period from this.

>> No good.  You should split them up by perhaps 0.1 second.  See below.

 B) Write an equation for the function expressing the riders' height from the ground (h) as a function of time (t).
   I assume u have to find the amplitude, the period, and the mid line, and put it into the equation: y= a sin(bx)+d
but i don't know how to do this with the given information.
  
   *** I am having a lot of trouble with this and i would just like to thank you so much ahead of time for taking the time to help me with this problem.Thank you soo much!

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Ok, let's get to work.  I think the bungee oscillates between  y = 10 and y = 25, so the midpoint about which it oscillates is at  y = 17.5.  (That would be your 'd')

It starts at  y = 10 = -7.5 + 17.5   (the low point)

So your a = -7.5,  and you want COSINE not sine, because you are starting at 1, not at zero.

We are almost there:   y = -7.5 cos(bt) + 17.5

And the b = pi, because it takes 2 seconds to do one cycle.  so we need  bt = b(2) = 2pi, or b = pi.

Your equation is: (tada!!!)

y = -7.5 cos(pi t) + 17.5