document.write( "Question 1194771: The top of a ladder 10 meters long rests on a vertical wall of a residential building while
\n" ); document.write( "the bottom rests on a horizontal ground. If the top slides down at the rate of 20 meters per
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Algebra.Com's Answer #827052 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "The top of a ladder 10 meters long rests on a vertical wall of a residential building
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document.write( "Let x = x(t) be horizontal distance from the wall of one lsadder endpontt \r\n" );
document.write( "and y = y(t) be vertical coordinate of the other endpoint.\r\n" );
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document.write( "Then from Pythagoras, the length of the ladder is\r\n" );
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document.write( "    x^2 + y^2 = 10^2.    (1)\r\n" );
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document.write( "Here x = x(t) and y = y(t) are functions of time, t.\r\n" );
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document.write( "Differentiate equation  (1)  over t.  You will get\r\n" );
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document.write( "    2x*x'(t) + 2y*y'(t) = 0,\r\n" );
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document.write( "hence\r\n" );
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document.write( "    y'(t) = - (x*x'(t))/y.\r\n" );
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document.write( "Evaluate it at the given values  x = 8 m,  x'(t) = 20 m/minute,  y =  =  =  = 6.\r\n" );
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document.write( "You will get  y'(t) = -  =  =  = 26  meters per minute.     ANSWER\r\n" );
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