A particle p moves from the A(0,4) to the point (10,-4). The particle P can travel the upper- half plane `{(x,y)|yge0}` at the speed of 1 m/s. The coordinates of a point on the axis, if the sum of the squares of the travel times of the upper-and lower -half planes is minimum are

Options

A. (1,0)
B. (2,0)
C. (4,0)
D. (5,0)

Answer

B

Explanation

Let the point on the the axis be (c,0). Sum of the square of travel times is

`T=((sqrt(c^2+16))/(1))^2+(sqrt((10-c)^2+16)/(2))^2`
`=c^2+16+(116+c^2-20c)/(4)`
`=(5)/(4)c^2-5c+45=(5)/(4)(c^2-4c+36)`
Therefore, T is minimum at `c=2`.