Question

A 15 ft ladder leans against a wall. The bottom of the ladder is 3 ft from the wall at time t=0 and slides away from the wall at a rate of 1 ft/sec. Find the velocity of the top of the ladder at time t=3. The velocity of the ladder at time t=3 is --ft/sec

Answer 1

Length of Ladder feet

Distance of Bottom of ladder from the wall feet

Bottom of ladder is sliding away from wall at the rate feet/sec

Let height of the top of the ladder at t=0 be H feet.

Situation is shown in figure below:

Using pythagorus theorem in the right angled triangle:

   ... Equation (1)

Put values:

feet

Now differentiate equation (1) with respect to t:

Use formula:

We get:

Here the length of ladder L is not changing with respect to time t so

Now put all values:

feet/sec

Negative sign indicates top of the ladder is moving in down direction.