A man of height H is standing in front of an inclined plane mirror at an angle `theta` from horizontal. The vertical separation between man and inclined plane is x. Man can see its complete image in length `(H(H+x)"sin"theta)/(H +2x)` of mirror .
(Given : x = H = 1m and `theta = 45^(@)`)

If man starts moving with velocity `1 ms^(-1)` along vertical, find out length of mirror at t = 1s in which he can see his complete image.

Options

A. `(3)/(10)m`
B. `(3sqrt(2))/(5)m`
C. `(3)/(5sqrt(2))`
D. `(3)/(5)`m

Answer

C

Explanation

In this case only x will change so required length of mirror =`(1(1+2)"sin"45^(@))/(1+2xx2)`
=`(3 xx (1)/(sqrt(2)))/(5) = (3)/(5sqrt(2))m`