Practice AP question.

[evlangel164]

My teacher gives up released AP tests to practice so I'm working on the 2002 AP calculus BC question 3.

http://www.collegeboard.com/prod_downlo ... ulus%20bc'

you can go there to see the question. it's problem 3.

anyway, my problem is that i need to find the acceleration vector when the horizontal position is x=140

so i've gotten as far as 10t+4sin(t)-140=0

I don't know how to solve for t.

I know the answer is 13.647, but I'm not sure how they got it and I don't have a TI-89 to do it on. I only have a TI-83. How would I do this problem using my calculator?

If I know how to find t then I can do the rest on my own. Thank you =)

 

[stapel]

Note: It is generally considered courteous to post the exercise in question, rather than requiring others to go find it and post it for you.

Thank you.

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3) The path travelled by a particular car on a roller coaster may be modelled by:

. . . . .x(t) = 10t + 4sin(t)

. . . . .y(t) = (20 - t)(1 - cos(t))

The parameter "t" is measured in "seconds" over the interval 0 < t < 18 and "x" and "y" are measured in "meters".

The derivatives are given by:

. . . . .x'(t) = 10 + 4cos(t)

. . . . .y'(t) = (20 - t)sin(t) + cos(t) - 1

a) Find the slope of the path at time t = 2. Show your computations.

b) Find the car's acceleration vector at the time when the car's horizontal position is x = 140.

c) Find the time t at which the car is at its maximum height, and find the speed, in meters per second, of the car at this time.

d) For 0 < t < 18, there are two times when the car is at ground level. Find these two times and write an expression that gives the average speed, in meters per second, of the car between those two times. Do not evaluate the expression.