# Thread: Differential Equation Application, Prosecution Problem..PLZ HELP

1. ## Differential Equation Application, Prosecution Problem..PLZ HELP

Okay so the Percution problem is this... sorry for my english

A destroyer is in the middle of a heavy fog that vanishes for instance and lets you see an enemy submarine in the surface at 4km of distance.
Assume:
a) The submarine immersed instantly and moves on to an unknown direction.
b) The destroyer travels 3km in straight line to the submarine.
What trajectory should the destroyer fallow to be sure that it will pass directly over the submarine, if its speed v is three times the submarines?

2. Originally Posted by mayur03
Okay so the Percution problem is this... sorry for my english

A destroyer is in the middle of a heavy fog that vanishes for instance and lets you see an enemy submarine in the surface at 4km of distance.
Assume:
a) The submarine immersed instantly and moves on to an unknown direction.
b) The destroyer travels 3km in straight line to the submarine.
What trajectory should the destroyer fallow to be sure that it will pass directly over the submarine, if its speed v is three times the submarines?

You will find a diagram helps.

Take the initial position of the sub as the origin and the point the destroyer reaches after travelling the 3km as $\displaystyle (1,0)$ and when it reaches this point as $\displaystyle t=0$.

The destroyerr must move on a tragectory such that $\displaystyle \dot{r}=0$, and its speed is a constant $\displaystyle 3$ (in what ever units we are using). Therefore:

$\displaystyle (\dot{r})^2+(r\dot{\theta})^2=9$

or:

$\displaystyle r \dot{\theta}=\sqrt{8}$

We also know that $\displaystyle r=t+1$, so:

$\displaystyle \dot{\theta}=\frac{\sqrt{8}}{t+1}$

etc.

CB