document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=518949>Question 518949</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A doctor squirts a small amount of liquid from a syringe vertically. If the liquid emerges with a velocity of 5.5 m/s how long does it take for the liquid to return to the level of the syringe and what is the maximum height it can reach? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #345346 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=345346\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the function:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D ALIGN=MIDDLE  ALT=\"h%28t%29+=+-4.9t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the function for determining the height (in meters) of an object (liquid in this case) propelled upwards with an initial velocity <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;\" >(in meters per second) from an initial height of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D ALIGN=MIDDLE  ALT=\"h%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in meters) at time t (in seconds).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D ALIGN=MIDDLE  ALT=\"h%28t%29+=+-4.9t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B0%5D+=+5.5 ALIGN=MIDDLE  ALT=\"v%5B0%5D+=+5.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D+=+0 ALIGN=MIDDLE  ALT=\"h%5B0%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+0 ALIGN=MIDDLE  ALT=\"h%28t%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the time, t, at which the liquid will return to its initial height.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-4.9t%5E2%2B5.5t ALIGN=MIDDLE  ALT=\"0+=+-4.9t%5E2%2B5.5t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor a t.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%28-4.9t%2B5.5%29+=+0 ALIGN=MIDDLE  ALT=\"t%28-4.9t%2B5.5%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero product rule.<BR>\n" );
document.write( "<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;\" > This is the initial state.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.9t%2B5.5+=+0 ALIGN=MIDDLE  ALT=\"-4.9t%2B5.5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for t.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.9t+=+5.5 ALIGN=MIDDLE  ALT=\"4.9t+=+5.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1.12 ALIGN=MIDDLE  ALT=\"t+=+1.12\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds to return to its initial height at the doctor's syringe.<BR>\n" );
document.write( "To find the maximum height of the object (liquid), you need to find the vertex of the parabola which is the graph of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9t%5E2%2B5.5t ALIGN=MIDDLE  ALT=\"h%28t%29+=+-4.9t%5E2%2B5.5t\"   DISABLED_style= \"max-width:90%; height:auto;\" > This graphs into a parabola that opens downward so its vertex will be the maximum height.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9t%5E2%2B5.5t ALIGN=MIDDLE  ALT=\"h%28t%29+=+-4.9t%5E2%2B5.5t\"   DISABLED_style= \"max-width:90%; height:auto;\" > The value of t at the vertex is given by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-b%2F2a ALIGN=MIDDLE  ALT=\"t+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > where b = 5.5 and a = -4.9<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-5.5%29%2F2%28-4.9%29 ALIGN=MIDDLE  ALT=\"t+=+%28-5.5%29%2F2%28-4.9%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+=+0.56 ALIGN=MIDDLE  ALT=\"t+=+0.56\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds.  This is the time at which the object reaches its maximum height.  Substitute this into the function for the height to find the maximum height in meters.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%280.56%29+=+-4.9%280.56%29%5E2%2B5.5%280.56%29 ALIGN=MIDDLE  ALT=\"h%280.56%29+=+-4.9%280.56%29%5E2%2B5.5%280.56%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%280.56%29+=+1.54 ALIGN=MIDDLE  ALT=\"h%280.56%29+=+1.54\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );