Expert: Steve Holleran - 3/3/2008

Question
Please Help me...i dont understand how to do these questions

A lifting body's flight path was measured at (0, 45000) (1000, 44500) (2000, 22875) where the first number in the pair is the distance horizontally from the drop point and the second the heigth, both in feet.

1) Find the equation of the function [rounded to the nearest ten thousandth) which satisfies the measurements.

2) How far horizontally will the lifting body be from the dropped point when it reaches the ground? (rounded to the nearest ten thousandth)


Answer
Hi Reyna,

Well, I'm not absolutely certain what the function should be here, but from all my experience in motion problems, I believe you want to use a quadratic form:

                      h = ax^2 + by + c.
Where h is the height at distance x.

If we do that, you can substitute the (x,h) numbers in and get:

I.  (0, 45000)--> 45000 = a(0^2) + b(0) + c so c = 45000

II. (1000, 44500)--> 44500 = a(1000^2) + b(1000) + 45000

gives    10^6 * a + 10^3 * b = -500.

III. (2000, 22875) --> 22875 = a(2000^2) + b(2000) + 45000

gives    4 * 10^6 * a + 2 * 10^3 * b = -22125



Now, multiply equation I by -2 and solve the system :

    -2 * 10^6 * a - 2 * 10^3 * b = 1000

     4 * 10^6 * a + 2 * 10^3 * b = -22125
    ---------------------------------------

     2 * 10^6 * a                = -21125

           so   a = -0.0105625

Then replacing this value back into eq II gives

         -10562.5 + 10^3 b = -500

so                        b = 10.0625

So the function is

  h = -0.0105625 x^2 + 10.0625 x + 45000

Then for the second part of the problem, set this = 0 and use the quadratic formula to solve (I used a program), and I believe you get

x = 2594.64.


Hope this was clear enough.

Steve