AboutPaul Klarreich Expertise All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions.
I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.
Experience I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.
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!
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.
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