Find the path of least time given these conditions? Starting point = (2,6) End point = (8,-3) Velocity above the line y=2 is 1 unit/second Velocity below the line y=2 is 7 units/second
There could be simpler way of doing this but, this is what I followed.
As the intermediate point must lie at the interface
Hence the general point must be
Path of Displacement is
Differentiating with respect to
Plotting this equation with the help of inbuilt graphics utility, gives us
Hence path with least time is through the point