SOLUTION: 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 meter

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Question 1194771: 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?

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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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?
~~~~~~~~~~~~~~~~~~~ 

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 = sqrt%28100+-+8%5E2%29 = sqrt%28100-64%29 = sqrt%2836%29 = 6.


You will get  y'(t) = - %288%2A20%29%2F6 = 160%2F6 = 80%2F3 = 26 2%2F3 meters per minute.     ANSWER

Solved.