Question

A ladder 5 metre in length is resting against a wall. The bottom of the ladder is pulled along the ground away from the ball at the rate of 1.5 m per second. The height of the ladder on the wall when the foot of the ladder is 4 m away from the wall decrease @ the rate of

Answer 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