# 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

##### 1 Answer

There could be simpler way of doing this but, this is what I followed.

#### Explanation:

As the intermediate point must lie at the interface

Hence the general point must be

Path of Displacement is

(a) Displacement

Time taken

(b) Displacement

Time taken

Total Time

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