A 10-ft ladder rests against a vertical wall. If the bottom of the

A 10-ft ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/sec, how fast, in ft/sec, is the top of the ladder sliding down the wall, at the instant when the bottom of the ladder is 6 ft from the wall? Answer with 2 decimal places. Type your answer in the space below.

3 answers

If the base of the ladder is x from the wall, and the top of the ladder is y high, then

x^2+y^2 = 10^2

x dx/dt + y dy/dt = 0

So, figure y when x=6 and just plug in the numbers to find dy/dt.

dy/dt=-y dy/dt/x