document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=22186>Question 22186</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am stuck on this problem.<BR>\n" );
document.write( "Jacob is standing at the edge of a 3000 foot deep canyon. He kicks a ball into the air with a initial upward velocity of 32 feet per second. when will the ball return to the height from which it was kicked?\r<BR>\n" );
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document.write( "I can get it to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29=+-16t%5E2%2B32t ALIGN=MIDDLE  ALT=\"h%28t%29=+-16t%5E2%2B32t\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but i get stuck trying to factor that. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #10769 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=10769\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general form of the equation for the height of an object propelled upward with an initial velocity of v<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > from an initial height of h<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%29 ALIGN=MIDDLE  ALT=\"0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2+%2B+v0t+%2B+h0 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2+%2B+v0t+%2B+h0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and since the depth of the canyon by which Jacob is standing is really irrelevant, your initial equation is correct. The initial height is zero feet.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2+%2B+32t ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2+%2B+32t\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Now you would like to find out at what time (t) will the ball return to its initial height of 0 ft.\r<BR>\n" );
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document.write( "Setting h(t) = 0 ft. you can write:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2+%2B+32t+=+0 ALIGN=MIDDLE  ALT=\"-16t%5E2+%2B+32t+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for t by factoring -16t from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%28t+-+2%29+=+0 ALIGN=MIDDLE  ALT=\"-16t%28t+-+2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero product principle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+-+2+=+0 ALIGN=MIDDLE  ALT=\"t+-+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 2 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+2 ALIGN=MIDDLE  ALT=\"t+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The ball will return to its initial height of 0 ft. in 2 seconds.\r<BR>\n" );
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document.write( "Check: Set t = 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%282%29+=+-16%282%5E2%29+%2B+32%282%29 ALIGN=MIDDLE  ALT=\"h%282%29+=+-16%282%5E2%29+%2B+32%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for h.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%282%29+=+-64+%2B+64 ALIGN=MIDDLE  ALT=\"h%282%29+=+-64+%2B+64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%282%29+=+0 ALIGN=MIDDLE  ALT=\"h%282%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft.<BR>\n" );
document.write( " </SPAN>\n" );
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