document.write( "Question 122762: Solve. \r
\n" ); document.write( "\n" ); document.write( "If a ball thrown vertically upward from a height of 5ft, with an initial velocity of 80 ft/s, it's height(h) after (t) second is given by h=-16t squared + 80t + 5. ow long does it take the ball to return to the ground?
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Algebra.Com's Answer #90120 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
When the ball hits the ground, this means \"h=0\" (in other words, the height is zero)\r
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\n" ); document.write( "\n" ); document.write( "\"h+=+-16t%5E2+%2B+80t+%2B+5\" Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( "\"0=+-16t%5E2+%2B+80t+%2B+5\" Plug in \"h=0\". \r
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\n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for t:\r
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\n" ); document.write( "\n" ); document.write( "Starting with the general quadratic\r
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\n" ); document.write( "\n" ); document.write( "\"at%5E2%2Bbt%2Bc=0\"\r
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\n" ); document.write( "\n" ); document.write( "the general solution using the quadratic equation is:\r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"\r
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\n" ); document.write( "\n" ); document.write( "So lets solve \"-16%2At%5E2%2B80%2At%2B5=0\" ( notice \"a=-16\", \"b=80\", and \"c=5\")\r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-80+%2B-+sqrt%28+%2880%29%5E2-4%2A-16%2A5+%29%29%2F%282%2A-16%29\" Plug in a=-16, b=80, and c=5\r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-80+%2B-+sqrt%28+6400-4%2A-16%2A5+%29%29%2F%282%2A-16%29\" Square 80 to get 6400 \r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-80+%2B-+sqrt%28+6400%2B320+%29%29%2F%282%2A-16%29\" Multiply \"-4%2A5%2A-16\" to get \"320\"\r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-80+%2B-+sqrt%28+6720+%29%29%2F%282%2A-16%29\" Combine like terms in the radicand (everything under the square root)\r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-80+%2B-+8%2Asqrt%28105%29%29%2F%282%2A-16%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)\r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-80+%2B-+8%2Asqrt%28105%29%29%2F-32\" Multiply 2 and -16 to get -32\r
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\n" ); document.write( "\n" ); document.write( "So now the expression breaks down into two parts\r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-80+%2B+8%2Asqrt%28105%29%29%2F-32\" or \"t+=+%28-80+-+8%2Asqrt%28105%29%29%2F-32\"\r
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\n" ); document.write( "\n" ); document.write( "Now break up the fraction\r
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\n" ); document.write( "\n" ); document.write( "\"t=-80%2F-32%2B8%2Asqrt%28105%29%2F-32\" or \"t=-80%2F-32-8%2Asqrt%28105%29%2F-32\"\r
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\n" ); document.write( "\n" ); document.write( "Simplify\r
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\n" ); document.write( "\n" ); document.write( "\"t=5+%2F+2-sqrt%28105%29%2F4\" or \"t=5+%2F+2%2Bsqrt%28105%29%2F4\"\r
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\n" ); document.write( "\n" ); document.write( "So these expressions approximate to\r
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\n" ); document.write( "\n" ); document.write( "\"t=-0.0617376914898995\" or \"t=5.0617376914899\"\r
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\n" ); document.write( "\n" ); document.write( "So our possible solutions are:\r
\n" ); document.write( "\n" ); document.write( "\"t=-0.0617376914898995\" or \"t=5.0617376914899\"\r
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\n" ); document.write( "\n" ); document.write( "However, since a negative time doesn't make sense, our only solution is \r
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\n" ); document.write( "\n" ); document.write( "\"t=5.0617376914899\"\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So at around 5.06 seconds, the ball will hit the ground.
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