Wile E Coyote vs Road Runner: Racing for a Catch!

[lionsgirl12]

1. Wile E Coyote, armed with ACME^TM-brand rocket-propelled rollerblades, is at it again trying to catch his nemesis Road Runner. Suppose the ground velocities, in hundred miles per hour, of the twosome are described by the equations below:
Wile E Coyote: v'=200-8v²
Road Runner: v'=160-5v²

(a) Without solving the 2 equations, determine whether Wile E could (finally) catch Road Runner. What is his maximum velocity (i.e. his limiting velocity)?
(b) Solve Wile E's equation to find his velocity as a function of time. You may leave your answer in implicit form.

Homework Equations

3.
(a)v_L = $$\sqrt{200/8}$$
v_L = 5 mi/hr

(b) i know for this question you have to apply impartial fractions to find the solution but i need help setting it up

 

[gabbagabbahey]

L[/SUB] = $$\sqrt{200/8}$$
v_L = 5 mi/hr

Careful, $v$ is measured in hundreds of miles/hour

(b) i know for this question you have to apply impartial fractions to find the solution but i need help setting it up


[/b]

Well, what kind of differential equation is $\frac{dv}{dt}=200-8v^2$? (is it ordinary? what is its order? Is it separable?) What method(s) have you been taught to solve that type of DE?