document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1066608>Question 1066608</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I am having problems with one of my algebra 2 questions. It says that I need to create a function that will give me the minimum initial upward velocity, v, required to launch water to any given height. \r<BR>\n" );
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document.write( "Previously, I solved the first part of it using the vertical motion formula and got V=16t+h/t, but the formula is not the minimum velocity, so I need help figuring out the steps to find that out. I don't want the answer, but rather a point in the right direction. \r<BR>\n" );
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document.write( "Thank you in advance! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #681790 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=681790\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Launching against gravity from ground level,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+-16t%5E2+%2B+v%5B0%5D%2At+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+-16t%5E2+%2B+v%5B0%5D%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Units are feet and seconds. The 1st term is the <BR>\n" );
document.write( "effect of gravity. The 2nd term is the effect of<BR>\n" );
document.write( "launch speed. I can solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+v%5B0%5D+ ALIGN=MIDDLE  ALT=\"+v%5B0%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+v%5B0%5D%2At+=+h%28t%29+%2B+16t%5E2+ ALIGN=MIDDLE  ALT=\"+v%5B0%5D%2At+=+h%28t%29+%2B+16t%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+v%5B0%5D+=+h%28t%29%2Ft+%2B+16t+ ALIGN=MIDDLE  ALT=\"+v%5B0%5D+=+h%28t%29%2Ft+%2B+16t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'm not sure what they mean. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+v%5B0%5D+ ALIGN=MIDDLE  ALT=\"+v%5B0%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > would be <BR>\n" );
document.write( "minimum velocity needed to launch to at least <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+ ALIGN=MIDDLE  ALT=\"+h+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you plot <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+v%5B0%5D+ ALIGN=MIDDLE  ALT=\"+v%5B0%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a variable on the y-axis, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the horizontal axis, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+ ALIGN=MIDDLE  ALT=\"+h+\"   DISABLED_style= \"max-width:90%; height:auto;\" > remains fixed,<BR>\n" );
document.write( "( no longer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+ ALIGN=MIDDLE  ALT=\"+h%28t%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > )<BR>\n" );
document.write( "then you have a function with a minimum.<BR>\n" );
document.write( "I'll do a plot with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+100+ ALIGN=MIDDLE  ALT=\"+h+=+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-10%2C+10%2C+-20%2C+200%2C+100%2Fx+%2B+16x+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-20%2C+200%2C+100%2Fx+%2B+16x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Every point on the curve is ( t, v[0] ) that will let me<BR>\n" );
document.write( "reach <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+100+ ALIGN=MIDDLE  ALT=\"+h+=+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft. <BR>\n" );
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document.write( "This is my attempt to figure out what they<BR>\n" );
document.write( "mean by minimum velocity. By all means get<BR>\n" );
document.write( "other input on this\r<BR>\n" );
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