document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=17128>Question 17128</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You fire a rifle straight up. Your bullet leaves your fun at a velocity of 960 feet per second. Ignore air resistance. Consider the mussle of you gun to be at height zero. The bullet will reach its maxium altitude of __ feet after __ seconds. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #8304 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=8304\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I believe the formula for this is \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-16t%5E2+%2B+960+t+ ALIGN=MIDDLE  ALT=\"y=+-16t%5E2+%2B+960+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where y is the number of feet above the ground t seconds after firing, assuming gravitational constant of -32 ft/sec^2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Soooo, \r<BR>\n" );
document.write( "\n" );
document.write( "Where, y=0 are the two points where the bullet is at ground level.  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-16t%5E2+%2B+960t ALIGN=MIDDLE  ALT=\"+0+=+-16t%5E2+%2B+960t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Factor the common factors of 16t, and while you are at it, why not take out a -16t.  That's even better.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-16t%28t+-+60%29 ALIGN=MIDDLE  ALT=\"0+=+-16t%28t+-+60%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "t= 0 and t=60 seconds.   \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first value t=0 represents the time when the gun was fired, and the bullet left the gun.  The second time t=60 seconds represents the time when the bullet came back down to ground level.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "By symmetry, the bullet spends half the time going up, and half the time coming back down.  So the bullet reaches its maximum altitude at t= 30 seconds.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Maximum height attained is \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-16t%5E2%2B+960t ALIGN=MIDDLE  ALT=\"y+=+-16t%5E2%2B+960t\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where t= 30 seconds<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-16%2A30%5E2%2B+960%2A30+=+14400+ ALIGN=MIDDLE  ALT=\"y+=+-16%2A30%5E2%2B+960%2A30+=+14400+\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Check with a calculator:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28300%2C1000%2C+-10%2C70%2C+-10%2C+15000%2C+-16x%5E2%2B+960x%29 ALIGN=MIDDLE  ALT=\"graph+%28300%2C1000%2C+-10%2C70%2C+-10%2C+15000%2C+-16x%5E2%2B+960x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(Notice that on the y axis of this graph, the ten thousands digit is not displayed.  Sorry about that.  Still a pretty nice graph if you will correct that minor error by algebra.com graphing.) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "R^2 at SCC  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );