Question #35f3f

1 Answer
Mar 24, 2015

The rate is 656m/min=1056m/min10.83m/min

This is a nice example of a Related Rates problem. (Perhaps better called by the full name "Related Rates of Change")

Solution:
h is the distance from the floor to the end of the ladder.

l is the length of the ladder.
dldt=10m/min

We need to find dhdt

The relationship between the variables, h and l is given by the Pythagorean Theorem:

h2+52=l2

We need to find dhdt

To find the relationship between the rates of change, differentiate (implicitly) with respect to t.

2hdhdt+0=2ldldt

So:

hdhdt=ldldt

Substitute what we know and solve for the desired value.

We are told that dldt=10m/min and we are interested in
the instant when l=13m, but we also need h at that instant.

Using Pythagoras to find h when l=13m
h2+52=132
h2=144
h=12m

Now we can finish:

hdhdt=ldldt so at the instant we were asked about:

12mdhdt=13m(10m/min)

Thus
dhdt=13012m/min=656m/min=1056m/min10.83m/min