Answer to Question #177111 in Calculus for Thomas

Question

A 10 metres long ladder is being pushed towards the side of a wall. The bottom of the ladder is moving toward the wall at a rate of 0.1 meters per second. How fast is the top of the ladder moving up the wall when the bottom of the ladder is 6 meters from the wall?

Use the definition of derivative to find the derivative of h(t) = √ 2x − 1.

Answer 1

Given :

length of ladder=L=10m

distance of bottom of ladder from wall=x=6m

Top of ladder from ground=h

Here we can find h hy pythagoras theorem,

$\boxed{L^2=x^2+h^2}$

From this we get h=8m

Now , we have to find rate of change of h w.r.t time t.

On differentiating pythagoras theorem we get, (given L is constant)

$$2l{dl\over dt}=2x{dx\over dt}+2h{dh\over dt}$$

$$\\0=2(6)(-0.1)+2(8)({dh\over dt})$$

$$({dh\over dt})={3\over 4}(0.1)=0.075$$

There fore rate of change of top is 0.075 m/s