document.write( "Question 1156002: Please help me with this related rates question
\n" ); document.write( "The top of a ladder slides down a vertical wall at a rate of 0.125 m/s. At the moment when the bottom of the ladder is 5 m from the wall, it slides away from the wall at a rate of 0.3 m/s. How long is the ladder? \n" ); document.write( "

Algebra.Com's Answer #778692 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "We let the ladder slip down the wall, then we \r\n" );
document.write( "\"freeze\" it at an instant.\r\n" );
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document.write( "z is the length of the ladder, so it is constant.\r\n" );
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document.write( "y is a variable speed, getting shorter and shorter with \r\n" );
document.write( "respect to time.\r\n" );
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document.write( "dy/dt is a variable speed, getting faster and faster due \r\n" );
document.write( "to gravity, with respect to time. \r\n" );
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document.write( "x is a variable getting longer with respect to time.\r\n" );
document.write( "dx/dt is a variable, getting slower and slower. \r\n" );
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document.write( "[Important: do not make the mistake of substituting the \r\n" );
document.write( "\"freezing' value of the variables x, until we \r\n" );
document.write( "have done the calculus letting them vary. Leave the variables\r\n" );
document.write( "as they are until we have taken derivatives.]\r\n" );
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document.write( "We use the Pythagorean theorem:\r\n" );
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document.write( "We take derivatives with respect to t (time), remembering\r\n" );
document.write( "that since the length of the ladder z is the ONLY constant, \r\n" );
document.write( "the derivative of z² is 0.\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "Now that we have taken the derivative we can substitute the \r\n" );
document.write( "\"freezing\" values:\r\n" );
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document.write( "We are given that the top of a ladder slides down the\r\n" );
document.write( "wall at a rate of 0.125 m/s, since y is getting shorter,\r\n" );
document.write( "the rate y is changing is negative or -0.125 m/s.\r\n" );
document.write( "We \"freeze\" the variable x at 5 m. We \"freeze\" dx/dt at\r\n" );
document.write( "0.3 m/s.\r\n" );
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document.write( "So the \"freezing\" value of y is 12 m.\r\n" );
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document.write( "Now we can calculate the length of the ladder z\r\n" );
document.write( "from the Pythagorean theorem:\r\n" );
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document.write( "So the ladder is 13 m long.\r\n" );
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document.write( "Edwin

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