The rate of increase of length of the shadow of a man 2 metres height, due to a lamp at 10 metres height, when he is moving away from it at the rate of 2m/sec, is

Options

A. `(1)/(2)m//sec`
B. `(2)/(5) m//sec`
C. `(1)/(3)m//sec`
D. `5 m//sec`

Answer

A

Explanation

Let CE = y be the length of the shadow of the man at time t when he is x metres away from the lamp-post.
It given that `(dx)/(dt)=2 m//sec`
Clearly. `DeltaABE ~ DeltaCDE`

`implies (AB)/(CD)=(AE)/(CE)`
`implies (10)/(2)=(x+y)/(y)`
implies 4y = x
`implies (dy)/(dt)=(dx)/(dt)`
`implies (dy)/(dt)=(2)/(4)=(1)/(2) m//sec`