document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=56060>Question 56060</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.  A person dives from a 30 foot platform with an initial velocity of <BR>\n" );
document.write( "> 5 feet per second (upward)<BR>\n" );
document.write( "><BR>\n" );
document.write( ">         a.      Find the position of the function<BR>\n" );
document.write( ">         b.      How long will it take for the diver to hit the water?<BR>\n" );
document.write( ">         c.      What is the diver's velocity at impact?<BR>\n" );
document.write( ">         d.      What is the diver's acceleration at impact?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #38032 by </B><A HREF=/tutors/aboutme.mpl?userid=jenrobrody><B>jenrobrody(19)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jenrobrody><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=38032\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For a falling body problem, use the function:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=0.5ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"f%28x%29=0.5ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where a represents the acceleration due to gravity= -32 ft/sec^2<BR>\n" );
document.write( "b represents initial velocity= 5<BR>\n" );
document.write( "c represents initial height= 30<BR>\n" );
document.write( "(notice that up is positive and down is negative here)<BR>\n" );
document.write( "the function f(x)= -16x^2+ 5x + 30, gives the position of the diver at time t.<BR>\n" );
document.write( "Note that if x=0, f(0) = 30.  ie, the diver is 30 feet above water at t=0.<BR>\n" );
document.write( "We need to find time=x when f(x)=0.  ie, at zero height above water.<BR>\n" );
document.write( "Sovle for x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16x%5E2%2B5x%2B30=0 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B5x%2B30=0\"   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-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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-5+%2B-+sqrt%28+5%5E2-4%28-16%29%2830%29%29%29%2F%282%28-16%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-5+%2B-+sqrt%28+5%5E2-4%28-16%29%2830%29%29%29%2F%282%28-16%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=x+=+%28-5+%2B-+sqrt%28+25%2B1920%29%29%2F-32+ ALIGN=MIDDLE  ALT=\"x+=+%28-5+%2B-+sqrt%28+25%2B1920%29%29%2F-32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-5+%2B-+44.1%29%2F-32 ALIGN=MIDDLE  ALT=\"x+=+%28-5+%2B-+44.1%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = -49.1/-32 or 39.1/-32<BR>\n" );
document.write( "x = 1.5 or -1.2 seconds<BR>\n" );
document.write( "Use the positive answer for time after jumping.<BR>\n" );
document.write( "For the velocity, use the equation(same constants a,b,c as above):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=ax%2Bb ALIGN=MIDDLE  ALT=\"g%28x%29=ax%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or g(x)=(-32)x+5 = -32x + 5<BR>\n" );
document.write( "where g(x) represents the velocity after x seconds.<BR>\n" );
document.write( "Find velocity after 1.5 seconds:<BR>\n" );
document.write( "g(1.5) = -32(1.5) + 5 =  -43 feet/sec<BR>\n" );
document.write( "For acceleration, h(x)= a or, h(x)= -32 feet/sec^2<BR>\n" );
document.write( "acceleration is a constant and equals -32 feet/sec^2.<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );