Hello MHF! I am not sure I posted this question in the right section but this was my best guess.

I will start by saying I'm from Sweden and I apologize for my rather poor English, especially when it comes to math-language.

The problem I have a question about is based on a physics thesis for the way light breaks in water.

It is linked to a picture, which you can study here:Picture

The description is: A boy will run to his girlfriend standing on the other side of a pool. He must therefore run a part on land and also swim one part in water.

The task is:

1) How will this happen so that the boy will reach his girlfriend as fast as possible? The boy's speed on land is 10 m/s (meters per second) and his speed swimming is 2 m/s.

2) What is the relationship between the angles of theiandband the velocitiesv1andv2for the period to be as small as possible?

Now, I have solved 2) and I found out that the relationship is:

$\displaystyle \frac{sin(i)}{sin(b)}=\frac{v_{1}}{v_{2}}$

From the calculations to get to that conclusion I know that:

$\displaystyle sin(i)=\frac{x}{\sqrt{x^{2}+100}}$

and

$\displaystyle sin(b)=\frac{x}{\sqrt{100+(20-x)^{2}}}$

x is the horizontal line from the upper left corner of the pool to the point where the boy reaches the pool.

I now have an equation that looks like this to solve 1):

(when $\displaystyle v_{1}=10$ and $\displaystyle v_{2}=2$)

$\displaystyle \frac{\frac{x}{\sqrt{x^{2}+100}}}{\frac{x}{\sqrt{1 00+(20-x)^{2}}}}=\frac{10}{2}$

Is there anyone here on this splendid forum who has clue how to solve this? Or have I done this way to difficult for myself? I feels like there is an easier way of solving the problem but I can't find the way.

I am forever grateful for all the help I can get, even if it's only a mere though/suggestion!

Thanks in advance

Regards

Liljeros