Question

10. A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled
along the ground, away from the wall, at the rate of 2cm/s. How fast is its height
on the wall decreasing when the foot of the ladder is 4 m away from the wall ?​

Answer 1

Answer:Step 1:

Given :

The length of the ladder is l=5m

dxdt=2cm/s

The distance of the foot of the ladder from the foot x=4m

The height of the wall is y=52−42−−−−−−√=3

(By pythagoras theorem)

When x=5,y=3

Also x2+y2=52

Step 2:

Differentiating w.r.t t on both sides we get,

2x×dxdt+2y.dydt=0

⇒x.dxdt+y.dydt=0

Step 3:

Now substituting the values for x,y and dxdt we get,

4×2+3×dydt=0

⇒dydt=−83cm/s

Hence the height of the ladder on the wall decrease at the rate of 83cm/s

Step-by-step explanation:

Answer 2

The height is decreasing at the rate of

=8/3 cm per sec