ok so theres a roller coaster being built in the shape of a sinusoid, the high and low points on the track separated by 50 m horizontally and 30 m vertically, the lowest point is 3 m below the ground.

Question

my question is: the vertical timbers are spaced every 2m starting at x=0, and ending where the track goes below the ground. write a equation that prints out the length of each timber. the programs hould also print the total length of all vertical timbers so that you will knonw how much to purchase
x=39.76 (according to my calculations) when it reaches the ground

Answer 1

high and low points on the track separated by 30 m vertically
so, the amplitude is 30/2 = 15

high and low points on the track separated by 50 m horizontally
so, the period is 100 -- recall that sin(kx) has period 2π/k

So far, assuming we start at the top, we have y = 15cos(π/50 x)

Since the lowest point is 3m below ground, shift down by 3
y = 15cos(π/50 x) - 3

So, the kth pole (starting at k=0) has height
h(k) = 15cos(kπ/50 * 2) - 3
When does y=0? when π/50 x = π/2 -- x=25
So the sum of the heights of the first 26 poles is

25
∑ 15cos(π/50 * 2) - 3 = 390cos(π/25)-3 ≈ 383.295
k=0

So, what calculations did you make to get x=39.76? If you have an answer, it is nice to show how you got it. You may be right, but how will we know? You can check my work, but I can't check yours.

Answer 2

dang oobleck is a pro

Answer 3

oops. I see I made a couple of mistakes.
y=0 when 15cos(π/50 x) - 3 = 0, or x=21.8
So, we just need to add the first 21.8/2 = 11 poles.
10
∑ 15cos(π/50 * 2) - 3 = 90.19
k=0

Answer 4

ty this helped a lot, i made earlier calculations to solve but i think i put down enough info to solve the final problem