document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=471488>Question 471488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please provide detailed steps to solving the following word problem:\r<BR>\n" );
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document.write( "A ball is thrown upward with an intial velocity of 14 meters per second (mps) from a cliff that is 70 meters high. The height of the ball is given by the quadratic equation h = -4.9t^2 + 14t + 90 where h is in meters and t is the time in seconds since the ball was thrown. Find the time that the ball will be 20 meters from the ground...rounded to the nearest tenth of a second </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #323380 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=323380\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown upward with an initial velocity of 14 meters per second (mps)<BR>\n" );
document.write( " from a cliff that is 70 meters high. <BR>\n" );
document.write( "The height of the ball is given by the quadratic equation h = -4.9t^2 + 14t + 90 <BR>\n" );
document.write( "where h is in meters and t is the time in seconds since the ball was thrown.<BR>\n" );
document.write( " Find the time that the ball will be 20 meters from the ground...rounded to the nearest tenth of a second<BR>\n" );
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document.write( "Just take the given equation, replace h with 20 and you have:<BR>\n" );
document.write( "-4.9t^2 + 14t + 90 = 20<BR>\n" );
document.write( "arrange it into a quadratic equation<BR>\n" );
document.write( "-4.9t^2 + 14t + 90 - 20 = 0<BR>\n" );
document.write( "-4.9t^2 + 14t + 70 = 0<BR>\n" );
document.write( "Use the quadratic formula to find t<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "In this equation x=t; a=-4.9; b=14; c=70<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-14+%2B-+sqrt%2814%5E2-4%2A-4.9%2A70+%29%29%2F%282%2A-4.9%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-14+%2B-+sqrt%2814%5E2-4%2A-4.9%2A70+%29%29%2F%282%2A-4.9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-14+%2B-+sqrt%28196-%28-1372%29+%29%29%2F%28-9.8%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-14+%2B-+sqrt%28196-%28-1372%29+%29%29%2F%28-9.8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-14+%2B-+sqrt%28196%2B1372+%29%29%2F%28-9.8%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-14+%2B-+sqrt%28196%2B1372+%29%29%2F%28-9.8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-14+%2B-+sqrt%281568+%29%29%2F%28-9.8%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-14+%2B-+sqrt%281568+%29%29%2F%28-9.8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-14+%2B+39.6%29%2F%28-9.8%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-14+%2B+39.6%29%2F%28-9.8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25.6%2F%28-9.8%29 ALIGN=MIDDLE  ALT=\"25.6%2F%28-9.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = -2.6, obviously this is not the solution<BR>\n" );
document.write( "and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-14+-+39.6%29%2F%28-9.8%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-14+-+39.6%29%2F%28-9.8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-53.6%29%2F%28-9.8%29 ALIGN=MIDDLE  ALT=\"%28-53.6%29%2F%28-9.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 5.47 ~ 5.5 seconds it will be at 20 meter<BR>\n" );
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document.write( "You can prove this to yourself, substitute 5.47 for t in the original equation and see that h ~ 20m<BR>\n" );
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