(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A dog is at a distance L due north of a rabbit. He starts to pursue the rabbit and its motion always points to the rabbit. Given that the rabbit keeps running due east with a constant speed v and the dog's speed is a constant u, where v<u. Find the time that the dog catches the rabbit according to the method stated below.

(a) Consider the rabbit as a moving origin of a polar coordinates. Let [itex]\vec{r}[/itex] be the postition vector of dog relative to rabbit. Write down the velocity vectors relative to the rabbit along [itex]\vec{e_{r}}[/itex] [itex]\vec{e_{θ}}[/itex] respectively.

(b) Show that r=[itex]\frac{L (cot \frac{θ}{2})^\frac{u}{v}}{sinθ}[/itex]

(c) Use the result of (a) and (b) to find τ, the time for the dog to catch the rabbit.

[Hint: Consider the relation τ=[itex]\int dt[/itex] and dt= [itex]\frac{dθ}{dθ'}[/itex]]

2. Relevant equations

u speed of the dog

v speed of the rabbit

θ angle measure from east to the position of the dog.

L original dist. between the 2 animals

3. The attempt at a solution

For part (a), we can simply do it by resolving components.

I get [itex]\vec{v}[/itex]=<u+vcosθ, vsinθ>

But for part b and c, I have no idea.

We need to integrate [itex]\vec{v}[/itex] with repest to t in order to get [itex]\vec{r}[/itex], but in part a, [itex]\vec{v}[/itex] depends on θ only.

Alway, I don't know where can I use the hint.

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# Homework Help: A trace between a dog and a rabbit

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