document.write( "Question 1152042: A ball dropped from a height of 12 m and rebounds one half the distance on each bounce. What is the total distance it travels? \n" ); document.write( "

Algebra.Com's Answer #773933 by MathLover1(20850) $\"\"$ $\"About$

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Ball drops $\"12m\"$ in the first step.\r
\n" ); document.write( "\n" ); document.write( "It rebounds $\"6m\"$ and drops back $\"6m\"$ covering $\"12m\"$ in the second step.\r
\n" ); document.write( "\n" ); document.write( "It rebounds $\"3m\"$ and drops back $\"3m\"$ covering $\"6m\"$ in the third step.\r
\n" ); document.write( "\n" ); document.write( "This continues indefinitely.\r
\n" ); document.write( "\n" ); document.write( "Mathematically :\r
\n" ); document.write( "\n" ); document.write( " $\"S+=+12+%2B+12+%2B+6+%2B+3\"$ +... $\"infinity\"$ \r
\n" ); document.write( "\n" ); document.write( "= $\"12+\"$ + ( $\"12+%2B+6+%2B+3\"$ +... $\"infinity\"$ )\r
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\n" ); document.write( "\n" ); document.write( "Now ( $\"12+%2B+6+%2B+3\"$ +... $\"infinity\"$ ) is an infinite GP with $\"a+=+12\"$ and $\"r+=+1%2F2\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "=> $\"S+=+12+%2B+%2812%2F%281+-+1%2F2%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "=> $\"S+=+12+%2B+%2812%2F%281%2F2%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "=> $\"S+=+12+%2B+24%29\"$ \r
\n" ); document.write( "\n" ); document.write( "=> $\"S+=+36m\"$ \r
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