Question

A ladder 10 meters long rests on horizontal ground and leans against a vertical wall. The foot of the ladder is pulled away from the wall at the rate of 0.4 m/sec. How fast is the top sliding down the wall when the foot of the ladder is 6 m from the wall?

Answer 1

Answer:0.3 m/s

Step-by-step explanation:

Given

Length of ladder L=10 m

Foot of ladder is Pulled away at the rate of 0.4 m/s

Let the distance of foot of ladder be x m from origin and y be the distance of top of ladder from origin

from Pythagoras we can say that

`x^2+y^2=L^2`

differentiating w.r.t time we get

`2x\frac{\mathrm{d} x}{\mathrm{d} t}+2y\frac{\mathrm{d} y}{\mathrm{d} t}=0`

`x\frac{\mathrm{d} x}{\mathrm{d} t}+y\frac{\mathrm{d} y}{\mathrm{d} t}=0`

`x\frac{\mathrm{d} x}{\mathrm{d} t}=-y\frac{\mathrm{d} y}{\mathrm{d} t}`

and at x=6m , y=8 m using Pythagoras

`6* 0.4=-8* \frac{\mathrm{d} y}{\mathrm{d} t}`

`\frac{\mathrm{d} y}{\mathrm{d} t}=-0.3 m/s`

negative indicates that ladder is coming down