(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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A trace between a dog and a rabbit

**Physics Forums | Science Articles, Homework Help, Discussion**