A ft ladder leans against a wall. The bottom of the ladder is ft from the wall at time and slides away from the wall at a rate of .
Find the velocity of the top of the ladder at time .
The velocity of ladder at time is ft/sec.

2. lets denote the distance of the bottom of the ladder from the wall by x, and the distance of the upper end of the ladder from the floor by y, thus:

$y = \sqrt {17 - x^2 }$

now differentiate with respect to t:

$y' = - xx'\left( {17 - x^2 } \right)^{ - \frac{1}
{2}}$

we now that the bottom end of the ladder is moving with a constant speed of 3 ft/sec, thus:

$
x(t = 3) = x(t = 0) + 9 = 12ft$

....