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

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SUMMARY

Wile E Coyote's velocity, governed by the equation v' = 200 - 8v², has a limiting maximum velocity of 5 miles per hour, calculated using the formula vL = √(200/8). The Road Runner's velocity equation, v' = 160 - 5v², suggests that Wile E cannot catch him as the Road Runner's maximum velocity is higher. To find Wile E's velocity as a function of time, one must apply the method of partial fractions to solve the differential equation.

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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.



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

Careful, v 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 \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?
 

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