document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935484>Question 935484</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for the lovers of math:very very difficult algebra question:<BR>\n" );
document.write( "A company manufactures high-powered fountains that can be used to create elaborate water shows set to light  and   music.The  company makes three models of<BR>\n" );
document.write( "fountains, each of which can launch a vertical stream of water to a different height, as indicated in the table below.              Model A    Model B   Model C height          77            100           240 time to fall (s) 2.194,   ----,         ----  initial velocity 70.2 ,     ----,      123.9  complete the following tasks, filling in the missing values in the table as you find them:Find the time water would take to fall from each height in the table back to its starting level.Find the initial upward velocity required for fountain B to launch the water to its maximum heightCreate a function that will give you the minimum initial upward velocity ,v ,required to launch water to any given height , h. thank you<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 #568699 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=568699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Model......... A Model .B Model C Model<BR>\n" );
document.write( "height............. 77 ..100 ..240 <BR>\n" );
document.write( "time to fall (s) 2.194, ----, ----  <BR>\n" );
document.write( "initial velocity 70.2 , ----, 123.9 <BR>\n" );
document.write( "complete the following tasks, filling in the missing values in the table as you find them:<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Formula::<BR>\n" );
document.write( "height = -16*t^2 + vo*t<BR>\n" );
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document.write( "A Model:: 77 = x*2.194^2 + 70.2*2.194<BR>\n" );
document.write( "77 = -16*4.8136 + 154.019<BR>\n" );
document.write( "77 = 77<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "B Model::<BR>\n" );
document.write( "Cannot solve for both time to fall and initial velocity;<BR>\n" );
document.write( "one depends on the other<BR>\n" );
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document.write( "C Model::<BR>\n" );
document.write( "240 = -16t^2 + 123.9t<BR>\n" );
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document.write( "Solve for \"t\" using the quadratic formula.<BR>\n" );
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document.write( "Formula for minimum vo value::<BR>\n" );
document.write( "Since h(t) = -16t^2 + vo*t<BR>\n" );
document.write( "vo = (h+16t^2)/t = (h/t) + 16t<BR>\n" );
document.write( "---<BR>\n" );
document.write( "taking the derivative you get:<BR>\n" );
document.write( "vo' = h*(-1/t^2) + 16<BR>\n" );
document.write( "vo'= -h/t^2  +  16<BR>\n" );
document.write( "Minimum vp will occur when (-h/t^2) + 16 = 0<BR>\n" );
document.write( "Solving for \"t\" you get:<BR>\n" );
document.write( "h/t^2 = 16<BR>\n" );
document.write( "t^2 = 16h<BR>\n" );
document.write( "t = 4sqrt(h)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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