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Calculus/Pre Calculus -(Honors Advanced Math II class)
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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?
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, using 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!
Take y = asin(bx) + d.
At t=0 and t=2, the equation repeats.
Since the sin() repeats every 2π, take b as π.
The low is 10, the high is 25, so the center is at 35/2. This is the value for d.
Since they go up and down by 15, they go 15/2 up and 15/2 down. Take a = 15/2.
The overall equation is then 15•sin(πx)/2 + 35/2 = (15•sin(πx) + 35)/2.
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