A ladder 10 metres long rests with one end against a vertical wall, the other on the floor. The lower end moves away from the wall at the rate of 2 metres/minute. The rate at which the upper end falls when its base is 6 metres away from the wall

Options

A. 3 metres/min
B. 2/3 metres/min
C. 3/2 metres/min
D. none of these

Answer

C

Explanation

Let at time t the lower end P of ladder PQ be at a distance x metres from the wall and the upper end Q be at height y from the ground. Then,
`x^(2)+y^(2)=10^(2)`
It is given that `(dx)/(dt)=2`

We have to find `(dy)/(dt)` when x = 6
Putting x = 6 in `x^(2)+y^(2)=10^(2)`, we get y=8
Now,
`x^(2)+y^(2)=10^(2)`
`implies 2x(dx)/(dt)+2y(dy)/(dt)=0`
`implies 6xx2+8xx(dy)/(dt)=0 " "["Putting x = 6, y = 8 and "(dx)/(dt)=2]`
`implies (dy)/(dt)=-(3)/(2)` metres/min