t P 1 the steady state) 7) A Pursuit Problem. A dog walks north from a crossroad
ID: 2982574 • Letter: T
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t P 1 the steady state) 7) A Pursuit Problem. A dog walks north from a crossroads at 1 mile The dogs master begins one mile east of the crossroads and walks at all times directly at the dog with a constant speed of v miles per hour. Let y) be the position of the master at time t where x is measured east of the crossroads and y is measured north of the crossroads a) Find the position of the dog measured north from the crossroads at time t b) Find the direction (slope or dyldx) of the master as a function of the position of the master and the dog at time t. Solve for t in this equation. c) Differentiate the equation above with respect to x. d) Find the equation for the speed of the master in terms of dyldx and dx/dt. Solve this equation for dt/dx e) Substitute the result from (d) into the equation from (c) and simplify. This will give you a second order differential equation in terms of y and x alone. Solve the ODE from (e). g) When and where does the master overtake the dog if v 1.5? h) Find the function that gives the meeting time in terms of v.Explanation / Answer
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