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 the i and b and the velocities v1 and v2 for the period to be as small as possible?
Now, I have solved 2) and I found out that the relationship is:
From the calculations to get to that conclusion I know that:
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 and )
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