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The top of a ladder 10 meters long rests on a vertical wall of a residential building
while the bottom rests on a horizontal ground. If the top slides down at the rate
of 20 meters per minute, how fast is the lower end moves along the ground
when the lower end is 8 meters from the wall?
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Let x = x(t) be horizontal distance from the wall of one lsadder endpontt
and y = y(t) be vertical coordinate of the other endpoint.
Then from Pythagoras, the length of the ladder is
x^2 + y^2 = 10^2. (1)
Here x = x(t) and y = y(t) are functions of time, t.
Differentiate equation (1) over t. You will get
2x*x'(t) + 2y*y'(t) = 0,
hence
y'(t) = - (x*x'(t))/y.
Evaluate it at the given values x = 8 m, x'(t) = 20 m/minute, y = = = = 6.
You will get y'(t) = - = = = 26 meters per minute. ANSWER
Solved.