document.write( "Question 1193538: a 13 foot ladder leans against a wall. The foot of a ladder begins to slide away from the wall at the rate of 1 foot per minute. When the foot is 5ft from the wall, at what rate is the top of the ladder is falling?
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\n" ); document.write( "b.4/3 ft/min.
\n" ); document.write( "c.3/4 ft/min.
\n" ); document.write( "d.12/5 ft/min. \n" ); document.write( "

Algebra.Com's Answer #825601 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "a 13 foot ladder leans against a wall. The foot of a ladder begins to slide away from the wall
\n" ); document.write( "at the rate of 1 foot per minute. When the foot is 5ft from the wall, at what rate is the top
\n" ); document.write( "of the ladder is falling?
\n" ); document.write( "a.5/12 ft/min.
\n" ); document.write( "b.4/3 ft/min.
\n" ); document.write( "c.3/4 ft/min.
\n" ); document.write( "d.12/5 ft/min.
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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 = 13^2.    (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 = 5 ft,  x'(t) = 1 ft/minute,  y =  =  =  = 12.\r\n" );
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document.write( "You will get  y'(t) = -  = - 5/12 ft/minute.    \r\n" );
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document.write( "ANSWER.  The top of the ladder moves vertically down at the rate of 5/12 ft per minute.\r\n" );
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