Question

3. One end of 8 metres long ladder is resting on the
ground and another on the wall by 5 metres height
from the ground. If the ladder slips down 2 metres
from the wall, calculate the distance by which the
other end of the ladder slips on the ground.
roo long loddor is resting on the​

Answer 1

Explanation:

The required problem be,

Let, angle between floor and the ladder be θ

Let at any time

′

t

′

AB=xcm and BC=ycm

So,

sinθ=

500

x

and ,

cosθ=

500

y

or, x=500sinθ

or, y=500cosθ

Also given that

dt

dx

=10cm/s

implies that,

500.cosθ.

dt

dθ

=10

implies that,

dt

dθ

=

50cosθ

1

dt

dθ

=

50.

500

y

1

=

y

10

=

200

10

Hence the requires angle is

=

20

1

rad/s

Answer 2

Explanation:

A ladder 10 feet long

The picture looks like this.

We have dx/dt = 1 ft/sec, and we want dy/dt.

x and y are related by the Pythagorean Theorem

Differentiate both sides of this equation with respect to t to get

When x = 8 ft, we have

therefore

The top of the ladder is sliding down (because of the negative sign in the result) at a rate of 4/3 feet per second.