On one boundary of a swimming pool , there is a person at point `A` whose speed of running on group (boundary) is `10ms^(-1)` , while that of swimming is `6ms^(-1)` . He has to reach a point `B` in the swimming pool . The distance covered on the boundary so that the time required to reach the point `B` in the pool is minimum, is

Options

A. `10`m
B. `6`m
C. `7`m
D. `sqrt(116)`m

Answer

C

Explanation

Required time `t= (x)/(10) + ((sqrt4^(2) + (10-x)^(2)))/(5)` for minimum time `(dt)/(dx) = 0 implies x=7"m"`
OR
Just like light , he has different speeds on ground and in water , so to minimize the time, Fermat's principle must hold good.
`"Sin"theta_(C) = (6)/(10) = (3)/(5) implies theta_(C) = 37^(@) implies "tan"theta_(C) = (3)/(4) = (10-x)/(4) implies x=7"m"`