Pursuit Problem:(adsbygoogle = window.adsbygoogle || []).push({});

A Frisbee is 40 ft north and 30 ft east of a dog.

The Frisbee is traveling north at 5 ft sec.

The dog can run at constant 10 ft/sec = SQRT( (Vdx)^2 + (Vdy)^2 )

Tan(angle)=Y(t)/X(t)

As the dog runs towards the Frisbee, the dog from “instinct” keeps the angle constant by adjusting his Vdx and Vdy closing velocities.

What is the equation of the curve that the dog travels along in catching the Frisbee? Picking an arbitrary time, say 5 seconds, what are the X and Y values of the equation. What are Vdx, and Vdy at 5 seconds?

Does anyone have a solution to this problem?

Other obvious questions:

Is the arc length of the pursuit equation a minimum, when the angle is kept constant? Is the time to catch the Frisbee also a minimum?

Thanks for any help on this. (It has been 30 years since I’ve solved any DE’s)

Dr Bob

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# Frisbee Dog Pursuit Problem

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