document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=763698>Question 763698</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help please! I'm so confused by this problem. Can you explain it step by step?\r<BR>\n" );
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document.write( "if an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any time t is given by: h=-16t^2+vt+s<BR>\n" );
document.write( "(where h and s are in ft, t is in seconds and v is in ft/sec)<BR>\n" );
document.write( "a ball is thrown upward with an initial velocity of 96 ft/sec from the top of a 100 ft bridge. Determine the time that it takes for the ball to get to a height of 200 ft. <BR>\n" );
document.write( "Round answers to 2 decimals.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #464968 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=464968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+-16t%5E2%2Bvt%2Bs+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+-16t%5E2%2Bvt%2Bs+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "notice I replaced <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+ ALIGN=MIDDLE  ALT=\"+h+\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <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( "It's just a matter of preference.<BR>\n" );
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document.write( "Think of the 1st term as how the force<BR>\n" );
document.write( "of gravity is affecting the height.<BR>\n" );
document.write( "The other terms have nothing to do with gravity.<BR>\n" );
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document.write( "The 2nd term has to do with how fast you<BR>\n" );
document.write( "release the ball, and whether you throw it<BR>\n" );
document.write( "up or down (+) is for up, (-) is for down.<BR>\n" );
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document.write( "The 3rd term is only the height above ground<BR>\n" );
document.write( "from which the ball is released.<BR>\n" );
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document.write( "It's important to see that at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+0+ ALIGN=MIDDLE  ALT=\"+t+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, just<BR>\n" );
document.write( "as the ball is released, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%280%29+=+-16%2A0%5E2%2Bv%2A0%2Bs+ ALIGN=MIDDLE  ALT=\"+h%280%29+=+-16%2A0%5E2%2Bv%2A0%2Bs+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%280%29+=+s+ ALIGN=MIDDLE  ALT=\"+h%280%29+=+s+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the height from which ball is released,<BR>\n" );
document.write( "and you are given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+100+ ALIGN=MIDDLE  ALT=\"+s+=+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "You are asked to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+200+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+200+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft<BR>\n" );
document.write( "Note that the positive <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+96+ ALIGN=MIDDLE  ALT=\"+96+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft/sec has to fight <BR>\n" );
document.write( "against the negative <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16+ ALIGN=MIDDLE  ALT=\"+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft/sec2 which is acceleration<BR>\n" );
document.write( "due to gravity.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+200+=+-16t%5E2+%2B+96t+%2B+100+ ALIGN=MIDDLE  ALT=\"+200+=+-16t%5E2+%2B+96t+%2B+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-16t%5E2+%2B+96t+-+100+=+0+ ALIGN=MIDDLE  ALT=\"+-16t%5E2+%2B+96t+-+100+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4t%5E2+%2B+24t+-+25+=+0+ ALIGN=MIDDLE  ALT=\"+-4t%5E2+%2B+24t+-+25+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "use quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+t+=+%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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-4+ ALIGN=MIDDLE  ALT=\"+a+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+24+ ALIGN=MIDDLE  ALT=\"+b+=+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-25+ ALIGN=MIDDLE  ALT=\"+c+=+-25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+t+=+%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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28-24+%2B-+sqrt%28+24%5E2+-+4%2A%28-4%29%2A%28-25%29+%29%29+%2F+%282%2A%28-4%29%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28-24+%2B-+sqrt%28+24%5E2+-+4%2A%28-4%29%2A%28-25%29+%29%29+%2F+%282%2A%28-4%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28-24+%2B-+sqrt%28+576+-+400+%29%29+%2F+%28-8%29+%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28-24+%2B-+sqrt%28+576+-+400+%29%29+%2F+%28-8%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28-24+%2B-+sqrt%28+176+%29%29+%2F+%28-8%29+%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28-24+%2B-+sqrt%28+176+%29%29+%2F+%28-8%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28-24+%2B-+13.2665+%29+%2F+%28-8%29+%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28-24+%2B-+13.2665+%29+%2F+%28-8%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are 2 valid solutions. There is a height when <BR>\n" );
document.write( "the ball is on the way up to it's peak, and also a<BR>\n" );
document.write( "height when the ball is on the way down from it's peak.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+-24+%2B+13.2665+%29+%2F+%28-8%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-24+%2B+13.2665+%29+%2F+%28-8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+1.3417+ ALIGN=MIDDLE  ALT=\"+t+=+1.3417+\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec<BR>\n" );
document.write( "and, also<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+-24+-+13.2665+%29+%2F+%28-8%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-24+-+13.2665+%29+%2F+%28-8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+-37.2665+%2F+%28-8%29+ ALIGN=MIDDLE  ALT=\"+t+=+-37.2665+%2F+%28-8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+4.6583+ ALIGN=MIDDLE  ALT=\"+t+=+4.6583+\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec<BR>\n" );
document.write( "( note that you should never end up with a negative time )<BR>\n" );
document.write( "Here's a plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-2%2C+20%2C+-20%2C+250%2C+-16x%5E2+%2B+96x+%2B+100+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-2%2C+20%2C+-20%2C+250%2C+-16x%5E2+%2B+96x+%2B+100+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At t = 1.34 sec the height is 200 ft and<BR>\n" );
document.write( "At t = 4.66 sec the height is 200 ft<BR>\n" );
document.write( "You can see this on plot<BR>\n" );
document.write( "Hope this helps\r<BR>\n" );
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document.write( " </SPAN>\n" );
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