PROBLEM STATEMENT:
The positions of four battle ships on the ocean are such that the ships form the vertices of a square of length L = 2l. At some instant each ship fires a missile that directs its motion steadily toward the missile on its right. Assuming that the four missiles fly horizontally and with the same speed, find the path of the missile shot from each of the ships.
ATTEMPTED SOLUTION:
I thought this problem was similar to the classic mice pursuit problem and as I had already derived the following relation for an N-gon I used it to get the trajectory of the missiles.
$r(\theta$) = $r_0e^{-\theta\tan(\frac{\pi}{N})}$ -(1)
In this case $N = 4$, this leads to (1) becoming
$r(\theta$) = $r_0e^{-\theta}$ -(2)
Now, I'm certain that (2) is the required equation that describes the trajectory of the missiles. However, the answer provided in my book is
$x-l$ $=$ $r_0cos(\theta)$ and $y-l$ $=$ $r_0sin(\theta)$
To clear my confusions, I searched online and the solution I found online (which yields the same answer as my book) seems to be valid.
Can someone please inform whether my solution is correct? And if my solution is correct can I arrive at the books answers from my answer by changing the polar coordinates of my answer to cartesian coordinates?
Any kind of help will be highly appreciated.