document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1005463>Question 1005463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using the formula h=-1/2gt^2+v(0)t+h(0) (the zero in the parens is lower/small beneath the letter) and g= gravitational constant and v = upward velocity from a starting height of h. <BR>\n" );
document.write( " 1a. What is the height after three seconds of a penny dropped from the roof of the a tall building about 1250 feet tall? <BR>\n" );
document.write( " 1b. After how many seconds does the penny hit the ground? <BR>\n" );
document.write( " 2. What is the height after three seconds of a ball thrown from the roof of a building about 495 feet tall and is tossed upwards with a velocity of 10m/s? <BR>\n" );
document.write( " 2b. After how many seconds does it hit the ground? <BR>\n" );
document.write( " Thanks in advance. I think I have the answers but want to check the work done. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #621730 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=621730\">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=-%281%2F2%29gt%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D ALIGN=MIDDLE  ALT=\"h=-%281%2F2%29gt%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a general formula.<BR>\n" );
document.write( " <BR>\n" );
document.write( "For the first problem we will set:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" >= time from the moment the penny is dropped (we will measure it in seconds, because it will be a short time),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D=1250 ALIGN=MIDDLE  ALT=\"h%5B0%5D=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" >= height (in feet) at the moment, <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;\" > , when the penny is dropped,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B0%5D=0 ALIGN=MIDDLE  ALT=\"v%5B0%5D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the initial velocity (in feet/second) of the penny 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;\" > (since it was \"dropped\", it was not thrown up or down with any initial velocity).<BR>\n" );
document.write( "We will use the acceleration of gravity in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ft%2Fsecond%5E2 ALIGN=MIDDLE  ALT=\"ft%2Fsecond%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , to agree with the other units:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g=32 ALIGN=MIDDLE  ALT=\"g=32\"   DISABLED_style= \"max-width:90%; height:auto;\" > = acceleration of gravity in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ft%2Fsecond%5E2 ALIGN=MIDDLE  ALT=\"ft%2Fsecond%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Substituting, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-%281%2F2%2932t%5E2%2B0%2At%2B1250 ALIGN=MIDDLE  ALT=\"h=-%281%2F2%2932t%5E2%2B0%2At%2B1250\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-16t%5E2%2B1250 ALIGN=MIDDLE  ALT=\"h=-16t%5E2%2B1250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "1a. For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3 ALIGN=MIDDLE  ALT=\"t=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-16%2A3%5E2%2B1250=-16%2A9%2B1250=-144%2B1250=1106 ALIGN=MIDDLE  ALT=\"h=-16%2A3%5E2%2B1250=-16%2A9%2B1250=-144%2B1250=1106\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the height of the penny after three seconds is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281106feet%29 ALIGN=MIDDLE  ALT=\"highlight%281106feet%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "1b. When the penny hits the ground, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > . Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-16t%5E2%2B1250 ALIGN=MIDDLE  ALT=\"0=-16t%5E2%2B1250\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16t%5E2=1250 ALIGN=MIDDLE  ALT=\"16t%5E2=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2=1250%2F16 ALIGN=MIDDLE  ALT=\"t%5E2=1250%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2=78.125 ALIGN=MIDDLE  ALT=\"t%5E2=78.125\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=sqrt%2878.125%29 ALIGN=MIDDLE  ALT=\"t=sqrt%2878.125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=about+8.84 ALIGN=MIDDLE  ALT=\"t=about+8.84\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the penny hits the ground after about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%288.85seconds%29 ALIGN=MIDDLE  ALT=\"highlight%288.85seconds%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( " <BR>\n" );
document.write( "For the second problem we will set:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" >= time from the moment the ball is tossed (we will measure it in seconds, because it will be a short time),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B0%5D=10 ALIGN=MIDDLE  ALT=\"v%5B0%5D=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the initial velocity (in meters/second) of the ball 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;\" > (since it was \"dropped\", it was not thrown up or down with any initial velocity).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28IF%29 ALIGN=MIDDLE  ALT=\"red%28IF%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (as I originally misread) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D=495 ALIGN=MIDDLE  ALT=\"h%5B0%5D=495\"   DISABLED_style= \"max-width:90%; height:auto;\" >= height (in meters) at the moment, <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;\" > , when the ball is tossed,<BR>\n" );
document.write( "We will use the acceleration of gravity in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=meters%2Fsecond%5E2 ALIGN=MIDDLE  ALT=\"meters%2Fsecond%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , to agree with the other units:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g=9.8 ALIGN=MIDDLE  ALT=\"g=9.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = acceleration of gravity in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=meters%2Fsecond%5E2 ALIGN=MIDDLE  ALT=\"meters%2Fsecond%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Substituting, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-%281%2F2%299.8t%5E2%2B10t%2B495 ALIGN=MIDDLE  ALT=\"h=-%281%2F2%299.8t%5E2%2B10t%2B495\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-4.9t%5E2%2B10t%2B495 ALIGN=MIDDLE  ALT=\"h=-4.9t%5E2%2B10t%2B495\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3 ALIGN=MIDDLE  ALT=\"t=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-4.9%2A3%5E2%2B10%2A3%2B495 ALIGN=MIDDLE  ALT=\"h=-4.9%2A3%5E2%2B10%2A3%2B495\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-4.9%2A9%2B30%2B495 ALIGN=MIDDLE  ALT=\"h=-4.9%2A9%2B30%2B495\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-44.1%2B30%2B495 ALIGN=MIDDLE  ALT=\"h=-44.1%2B30%2B495\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=480.9 ALIGN=MIDDLE  ALT=\"h=480.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the height of the ball after three seconds is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28480.9meters%29 ALIGN=MIDDLE  ALT=\"highlight%28480.9meters%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "2b. When the ball hits the ground, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > . Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-4.9t%5E2%2B10t%2B495 ALIGN=MIDDLE  ALT=\"0=-4.9t%5E2%2B10t%2B495\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Solving the quadratic equation we get two solutions, but the negative solution does not make sense, and needs to be discarded.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-10+%2B+sqrt%2810%5E2-4%2A%28-4.9%29%2A495+%29%29%2F%282%2A4.9%29 ALIGN=MIDDLE  ALT=\"t=%28-10+%2B+sqrt%2810%5E2-4%2A%28-4.9%29%2A495+%29%29%2F%282%2A4.9%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=%28-10+%2B+sqrt%28100%2B9702%29%29%2F9.8 ALIGN=MIDDLE  ALT=\"t=%28-10+%2B+sqrt%28100%2B9702%29%29%2F9.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-10+%2B+sqrt%289802%29%29%2F9.8 ALIGN=MIDDLE  ALT=\"t=%28-10+%2B+sqrt%289802%29%29%2F9.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=about%28-10+%2B+99%29%2F9.8=89%2F9.8=about9.08 ALIGN=MIDDLE  ALT=\"t=about%28-10+%2B+99%29%2F9.8=89%2F9.8=about9.08\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the ball hits the ground after about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%289.08seconds%29 ALIGN=MIDDLE  ALT=\"highlight%289.08seconds%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28IF%29 ALIGN=MIDDLE  ALT=\"red%28IF%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > it was really meant as  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D=495 ALIGN=MIDDLE  ALT=\"h%5B0%5D=495\"   DISABLED_style= \"max-width:90%; height:auto;\" >= height (in feet),<BR>\n" );
document.write( "we have a units mismatch.<BR>\n" );
document.write( "We have to get everything in feet, or everything in meters.<BR>\n" );
document.write( "Since I am a supporter of the SI system of units, I will convert <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=495+feet ALIGN=MIDDLE  ALT=\"495+feet\"   DISABLED_style= \"max-width:90%; height:auto;\" > to meters.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=495+feet=%28495+feet%29%280.3048meters%2F%221+foot%22%29=150.9m ALIGN=MIDDLE  ALT=\"495+feet=%28495+feet%29%280.3048meters%2F%221+foot%22%29=150.9m\"   DISABLED_style= \"max-width:90%; height:auto;\" >(rounded), so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D=150.9 ALIGN=MIDDLE  ALT=\"h%5B0%5D=150.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >= height (in meters) at the moment, <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;\" > , when the ball is tossed,<BR>\n" );
document.write( "We will use the acceleration of gravity in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=meters%2Fsecond%5E2 ALIGN=MIDDLE  ALT=\"meters%2Fsecond%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , to agree with the other units:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g=9.8 ALIGN=MIDDLE  ALT=\"g=9.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = acceleration of gravity in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=meters%2Fsecond%5E2 ALIGN=MIDDLE  ALT=\"meters%2Fsecond%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Substituting, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-%281%2F2%299.8t%5E2%2B10t%2B150.9 ALIGN=MIDDLE  ALT=\"h=-%281%2F2%299.8t%5E2%2B10t%2B150.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-4.9t%5E2%2B10t%2B150.9 ALIGN=MIDDLE  ALT=\"h=-4.9t%5E2%2B10t%2B150.9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3 ALIGN=MIDDLE  ALT=\"t=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-4.9%2A3%5E2%2B10%2A3%2B150.9 ALIGN=MIDDLE  ALT=\"h=-4.9%2A3%5E2%2B10%2A3%2B150.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-4.9%2A9%2B30%2B150.9 ALIGN=MIDDLE  ALT=\"h=-4.9%2A9%2B30%2B150.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-44.1%2B30%2B495 ALIGN=MIDDLE  ALT=\"h=-44.1%2B30%2B495\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=136.8 ALIGN=MIDDLE  ALT=\"h=136.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the height of the ball after three seconds is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28136.8meters%29 ALIGN=MIDDLE  ALT=\"highlight%28136.8meters%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "2b. When the ball hits the ground, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > . Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-4.9t%5E2%2B10t%2B150.9 ALIGN=MIDDLE  ALT=\"0=-4.9t%5E2%2B10t%2B150.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Solving the quadratic equation we get two solutions, but the negative solution does not make sense, and needs to be discarded.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-10+%2B+sqrt%2810%5E2-4%2A%28-4.9%29%2A150.9+%29%29%2F%282%2A4.9%29 ALIGN=MIDDLE  ALT=\"t=%28-10+%2B+sqrt%2810%5E2-4%2A%28-4.9%29%2A150.9+%29%29%2F%282%2A4.9%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=%28-10+%2B+sqrt%28100%2B2957.6%29%29%2F9.8 ALIGN=MIDDLE  ALT=\"t=%28-10+%2B+sqrt%28100%2B2957.6%29%29%2F9.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-10+%2B+sqrt%283057.6%29%29%2F9.8 ALIGN=MIDDLE  ALT=\"t=%28-10+%2B+sqrt%283057.6%29%29%2F9.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=about%28-10+%2B+55.30%29%2F9.8=45.30%2F9.8=about4.62 ALIGN=MIDDLE  ALT=\"t=about%28-10+%2B+55.30%29%2F9.8=45.30%2F9.8=about4.62\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the ball hits the ground after about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%284.62seconds%29 ALIGN=MIDDLE  ALT=\"highlight%284.62seconds%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );