Let be the x axis the coast. The speed of an amphibian vehicle in the upper half-plane (land) is $v_{1}$ and in the under half-plane (sea) is $v_{2}$ and $v_{2}<v_{1}$. From the starting point (1,1) to the finish point(2,-3) which is the shortest road?
I still have no idea how to solve this problem I would appreciate any kind of help.
Let the point where the vehicle crosses the $x$ axis be $(a,0)$. Write the equation for the time taken by adding the time on land to the time on sea. You get the times by dividing the length of the path by the speed. Now differentiate the time with respect to $a$, set the derivative to zero, and solve.