document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133644>Question 133644</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618371834/algebrahomeworkh>mc dougal fl. algebra 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I have a chapter nine test tomarrow 4/26 and i need help!\r<BR>\n" );
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document.write( "ok..it has to do with quadrtatic equations..Vertical motion models: droped and thrown H=-16t squared + s      and -16t squared+vt+s\r<BR>\n" );
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document.write( "the question is.. A falcon dives toward a pigeon on the ground.<BR>\n" );
document.write( "when the falcon is at a height if 100 ft the pigeon sees the falcon. which is diving at a 220 ft per sec. estimate the time the pigeon has to escape.\r<BR>\n" );
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document.write( "h= height t= time s= initial height v= initial velocity\r<BR>\n" );
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document.write( "for some reason you also have to use the quaratic formlua <BR>\n" );
document.write( " -b +- squareroot of b squared - 4 (a)(C) over 2(a) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97800 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=97800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ok, remember up is positive, down is negative.  (it is that convention that causes us to put the negative sign on the lead coefficient in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-16t%5E2%2Bv%5B0%5Dt%2Bs%5B0%5D ALIGN=MIDDLE  ALT=\"h=-16t%5E2%2Bv%5B0%5Dt%2Bs%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Starting at 100 feet (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5B0%5D=100 ALIGN=MIDDLE  ALT=\"s%5B0%5D=100\"   DISABLED_style= \"max-width:90%; height:auto;\" > and starting at a velocity of 220 feet per second downward (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B0%5D=-220 ALIGN=MIDDLE  ALT=\"v%5B0%5D=-220\"   DISABLED_style= \"max-width:90%; height:auto;\" >) with an acceleration downward due to gravity of 16 ft per second per second (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2 ALIGN=MIDDLE  ALT=\"-16t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >), what is the time required for the falcon to reach 0 height (the ground).  I use <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5B0%5D ALIGN=MIDDLE  ALT=\"s%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > for initial velocity and distance because that is the value of those quantities at time <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B0%5D ALIGN=MIDDLE  ALT=\"t%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Just substitute the values to produce the following quadratic equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2-220t%2B100=0 ALIGN=MIDDLE  ALT=\"-16t%5E2-220t%2B100=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Just to make the numbers more manageable, divide the whole thing by -4 producing this equivalent quadratic equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4t%5E2%2B55t-25=0 ALIGN=MIDDLE  ALT=\"4t%5E2%2B55t-25=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Using the quadratic formula, <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;\" > with <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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=55 ALIGN=MIDDLE  ALT=\"b=55\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <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;\" > we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-55+%2B-+sqrt%2855%5E2-4%2A4%2A%28-25%29+%29%29%2F%282%2A4%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-55+%2B-+sqrt%2855%5E2-4%2A4%2A%28-25%29+%29%29%2F%282%2A4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-55+%2B-+sqrt%283025%2B400%29+%29%2F%288%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-55+%2B-+sqrt%283025%2B400%29+%29%2F%288%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-55+%2B-+sqrt%283425%29+%29%2F%288%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-55+%2B-+sqrt%283425%29+%29%2F%288%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3425=5%2A5%2A137 ALIGN=MIDDLE  ALT=\"3425=5%2A5%2A137\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283425%29=5%2Asqrt%28137%29 ALIGN=MIDDLE  ALT=\"sqrt%283425%29=5%2Asqrt%28137%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-55+%2B+5%2Asqrt%28137%29+%29%2F%288%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-55+%2B+5%2Asqrt%28137%29+%29%2F%288%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-55+-+5%2Asqrt%28137%29+%29%2F%288%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-55+-+5%2Asqrt%28137%29+%29%2F%288%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A little calculator work shows that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-55+-+5%2Asqrt%28137%29+%29%2F%288%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-55+-+5%2Asqrt%28137%29+%29%2F%288%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a little less than -14.  A negative result for a time measurement doesn't make any sense, so let's exclude this result as an extraneous root.\r<BR>\n" );
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document.write( "The calculator says that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-55+%2B+5%2Asqrt%28137%29+%29%2F%288%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-55+%2B+5%2Asqrt%28137%29+%29%2F%288%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a little over 0.44 seconds.  The pigeon has a little less than half a second to avoid becoming the falcon's lunch.\r<BR>\n" );
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document.write( "Of course, this calculation doesn't tell the whole story.  We would have to know how far a very frightened pigeon on the ground can move in 0.44 seconds, and then we would have to know something of the aerodynamics of a diving falcon -- specifically: can the falcon alter his trajectory in that time to compensate for the movement of the escaping pigeon? </SPAN>\n" );
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