Projectile Equation

[mathdad]

Let's go back to:

[MATH]c(2000)-(1+c^2)\left(\frac{9.81}{2}\right)\left(\frac{2000}{897}\right)^2>200[/MATH]
Get rid of the decimal value:

[MATH]2000c-(1+c^2)\left(\frac{981}{200}\right)\left(\frac{2000}{897}\right)^2>200[/MATH]
Divide through by 200:

[MATH]10c-(1+c^2)\left(\frac{981}{200}\right)\frac{20000}{897^2}>1[/MATH]
[MATH]10c-(1+c^2)\frac{98100}{897^2}>1[/MATH]
Multiply through by \(897^2=804609\):

[MATH]8046090c-(1+c^2)98100>804609[/MATH]
Arrange in standard form:

[MATH]98100c^2-8046090c+902709<0[/MATH]
Divide through by 9:

[MATH]10900c^2-894010c+100301<0[/MATH]
We know the solution will be the open interval between the roots, which I gave above.

Interesting breakdown of the question. I guess my answers for c are wrong. Hey, at least I tried.