document.write( "Question 1193215: A 10m ladder is leaning against a vertical wall with its foot on the same horizontal plane as the base of the wall. If the lower end of the ladder is moving away from the wall horizontally at 1m/sec, how fast is the top of the ladder descending when the lower end is 4 meters from the wall? \n" ); document.write( "

Algebra.Com's Answer #825275 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "A 10m ladder is leaning against a vertical wall with its foot on the same horizontal plane
\n" ); document.write( "as the base of the wall. If the lower end of the ladder is moving away from the wall
\n" ); document.write( "horizontally at 1m/sec, how fast is the top of the ladder descending when the lower end
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document.write( "Let x be horizontal distance from the wall and y be vertical coordinate.\r\n" );
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document.write( "Then from Pythagoras\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 = 4 m,  x'(t) = 1 m/s,  y =  =  = .\r\n" );
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document.write( "You will get  y'(t) = -  = - 0.436 m/s  (rounded).    ANSWER\r\n" );
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