SOLUTION: This is the problem that I have trouble solving. I have an idea of how to solve it but I am not sure where to beign to find the x cooridinates. You are riding on a roller coast

Question 32212: This is the problem that I have trouble solving. I have an idea of how to solve it but I am not sure where to beign to find the x cooridinates.
You are riding on a roller coaster whose path can be modeled by
y=.005x2(squared)-2x+200
where x and y are measured in feet. When t=0 sec, you are at the point (0,200) going downhill.
a. when t=4 sec, the y coordinate of your locations is 32. What is the x coordinate?
b. when t=4.23sec, the y coordinate of your location is 18. What is the y coordinate?
c.Use pythagorean theorem to approximate the lenght of the track between the two points.
d. what was the average speed betweem the two points?
Thanks.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
y=0.005x^2-2x+200
a)32=0.005x^2-2x+200
0=0.005x^2-2x+168
Graphing this I find x=120, giving the point (120,32)
b)18=0.005x^2 etc.
0 =0.005x^2-2x+182
Graphing this I find x=140, giving the point (140,18)
c) d=sqrt[(32-18)^2 + (120-140)^2]= 24.4 ft
d) The average is the distance divided by the time change:
ave.= 24.4 ft/ (0.23) sec. = 106.09 ft./sec.
Cheers,
stan H.

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