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

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In summary, Wile E Coyote is trying to catch Road Runner using ACMETM-brand rocket-propelled rollerblades. The equations for their ground velocities are v'=200-8v2 and v'=160-5v2. It is determined that Wile E's maximum velocity is 5 mi/hr and solving his equation using impartial fractions would require understanding of the type of differential equation and the methods used to solve it.
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lionsgirl12
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1. Wile E Coyote, armed with ACMETM-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)vL = [tex]\sqrt{200/8}[/tex]
vL = 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


 
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lionsgirl12;2872512(a)v[SUB said:
L[/SUB] = [tex]\sqrt{200/8}[/tex]
vL = 5 mi/hr

Careful, [itex]v[/itex] is measured in hundreds of miles/hour :wink:

(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 [itex]\frac{dv}{dt}=200-8v^2[/itex]? (is it ordinary? what is its order? Is it separable?) What method(s) have you been taught to solve that type of DE?
 

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

What is "Wile E Coyote vs Road Runner: Racing for a Catch!"?

"Wile E Coyote vs Road Runner: Racing for a Catch!" is a popular animated series that features the constant rivalry between Wile E Coyote, a failed predator, and Road Runner, a speedy bird. The series follows Wile E Coyote's attempts to catch and eat Road Runner, often resulting in comical and elaborate schemes.

Who created "Wile E Coyote vs Road Runner: Racing for a Catch!"?

The series was created by Chuck Jones for Warner Bros. Studios in 1949. Jones also directed and produced many of the episodes.

How many episodes are there in "Wile E Coyote vs Road Runner: Racing for a Catch!"?

There are a total of 48 episodes in the original series, which ran from 1949 to 1964. The series was then revived in 1971 and ran for an additional 14 episodes.

What is the running joke in "Wile E Coyote vs Road Runner: Racing for a Catch!"?

The running joke in the series is Wile E Coyote's constant failed attempts to catch and eat Road Runner. No matter how elaborate his plans or how many products he orders from the Acme Corporation, he always ends up getting hurt or outsmarted by Road Runner.

Why is "Wile E Coyote vs Road Runner: Racing for a Catch!" still popular today?

The series is still popular today because of its timeless humor and slapstick comedy. The constant back-and-forth between Wile E Coyote and Road Runner and the clever use of visual gags and wordplay make it entertaining for both children and adults. Additionally, the series has become a pop culture icon and has been referenced in various other forms of media.

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