document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176934>Question 176934</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131808672/algebrahomeworkh>Algebra 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I would like to know if you would be able to help me with this problem. <BR>\n" );
document.write( "using this equation:<BR>\n" );
document.write( "h= -16t^2+vt+c\r<BR>\n" );
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document.write( "Problem- a child tosses a ball upward with a starting velocity of 10 ft/s from a height of 3 ft.\r<BR>\n" );
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document.write( "b) solve. if not caught how long will the ball be in air? \r<BR>\n" );
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document.write( "Thank you for any help you can offer me!\r<BR>\n" );
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document.write( "Thank you so much!!\r<BR>\n" );
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document.write( "-j2012<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #131978 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=131978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since we have a \"starting velocity of 10 ft/s from a height of 3 ft\", this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=10 ALIGN=MIDDLE  ALT=\"v=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=3 ALIGN=MIDDLE  ALT=\"c=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=+-16t%5E2%2B10t%2B3 ALIGN=MIDDLE  ALT=\"h=+-16t%5E2%2B10t%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The ball will be in the air as long as the height h is NOT zero (when the ball is on the ground). So if we plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for t, we'll find when the ball hits the ground. From there, we can figure out how long it will be in the air.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=+-16t%5E2%2B10t%2B3 ALIGN=MIDDLE  ALT=\"h=+-16t%5E2%2B10t%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+-16t%5E2%2B10t%2B3 ALIGN=MIDDLE  ALT=\"0=+-16t%5E2%2B10t%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=at%5E2%2Bbt%2Bc ALIGN=MIDDLE  ALT=\"at%5E2%2Bbt%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-16 ALIGN=MIDDLE  ALT=\"a=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=10 ALIGN=MIDDLE  ALT=\"b=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=3 ALIGN=MIDDLE  ALT=\"c=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for t\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-%2810%29+%2B-+sqrt%28+%2810%29%5E2-4%28-16%29%283%29+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-%2810%29+%2B-+sqrt%28+%2810%29%5E2-4%28-16%29%283%29+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-16 ALIGN=MIDDLE  ALT=\"a=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=10 ALIGN=MIDDLE  ALT=\"b=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=3 ALIGN=MIDDLE  ALT=\"c=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-10+%2B-+sqrt%28+100-4%28-16%29%283%29+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-10+%2B-+sqrt%28+100-4%28-16%29%283%29+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-10+%2B-+sqrt%28+100--192+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-10+%2B-+sqrt%28+100--192+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28-16%29%283%29 ALIGN=MIDDLE  ALT=\"4%28-16%29%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-192 ALIGN=MIDDLE  ALT=\"-192\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-10+%2B-+sqrt%28+100%2B192+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-10+%2B-+sqrt%28+100%2B192+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28100--192%29 ALIGN=MIDDLE  ALT=\"sqrt%28100--192%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28100%2B192%29 ALIGN=MIDDLE  ALT=\"sqrt%28100%2B192%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-10+%2B-+sqrt%28+292+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-10+%2B-+sqrt%28+292+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=192 ALIGN=MIDDLE  ALT=\"192\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=292 ALIGN=MIDDLE  ALT=\"292\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-10+%2B-+sqrt%28+292+%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-10+%2B-+sqrt%28+292+%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32 ALIGN=MIDDLE  ALT=\"-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-10+%2B-+2%2Asqrt%2873%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-10+%2B-+2%2Asqrt%2873%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root  (note: If you need help with simplifying square roots, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-10%2B2%2Asqrt%2873%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-10%2B2%2Asqrt%2873%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-10-2%2Asqrt%2873%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-10-2%2Asqrt%2873%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-0.222 ALIGN=MIDDLE  ALT=\"t=-0.222\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0.847 ALIGN=MIDDLE  ALT=\"t=0.847\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use a calculator to approximate the answers.\r<BR>\n" );
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document.write( "Since a negative time value does NOT make sense, this means that the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0.847 ALIGN=MIDDLE  ALT=\"t=0.847\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So when the time is approximately 0.847 seconds, the ball will hit the ground. \r<BR>\n" );
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document.write( "So this means that the ball will be in the air for about 0.847 seconds. </SPAN>\n" );
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