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. If your answer is a number less than 1, place a leading "0" before the decimal point

Question

phi · Answer

Use Pythagoras to write
$$ x^2 + y^2 = 100 $$
use "implicit differentiation" to find the derivative of each variable with respect to t (i.e. time):
$$ 2 x \frac{dx}{dt} + 2y \frac{dy}{dt} = 0 $$
simplify , and substitute in the given numbers:
dx/dt = 1  (the sign depends on how we set up the problem.  See figure)
x=6
$$ y = \sqrt{100-36} = 8$$
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