document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1051000>Question 1051000</A>: <I><SPAN STYLE=\"word-break: break-all;\"> an object of mass 3kg is released from rest at 500m above ground, and allowed to fall under influence of gravity. the force due to air resistance is proportional to the velocity of the object with k=3N sec/m. formulate the particular explicit solution of the problem </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #666608 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=666608\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have the force of gravity acting towards the earth. <BR>\n" );
document.write( "You have the force of air resistance acting in the opposite direction.<BR>\n" );
document.write( "So summing the forces,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%28dv%2Fdt%29=-g%2Bkv ALIGN=MIDDLE  ALT=\"m%28dv%2Fdt%29=-g%2Bkv\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28dv%2Fdt%29-3v=-9.8 ALIGN=MIDDLE  ALT=\"3%28dv%2Fdt%29-3v=-9.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <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;\" ><BR>\n" );
document.write( "Solving that gives you,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%28t%29=%289.8%2F3%29%281-e%5E%28t%29%29 ALIGN=MIDDLE  ALT=\"v%28t%29=%289.8%2F3%29%281-e%5E%28t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now you have an equation for the velocity of the object. <BR>\n" );
document.write( "Integrate to get the equation for position,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28t%29=%289.8%2F3%29%28t-e%5E%28t%29%29%2BC ALIGN=MIDDLE  ALT=\"x%28t%29=%289.8%2F3%29%28t-e%5E%28t%29%29%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > with initial condition <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%280%29=500 ALIGN=MIDDLE  ALT=\"x%280%29=500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289.8%2F3%29%280-1%29%2BC=500 ALIGN=MIDDLE  ALT=\"%289.8%2F3%29%280-1%29%2BC=500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=500%2B9.8%2F3 ALIGN=MIDDLE  ALT=\"C=500%2B9.8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=1509.8%2F3 ALIGN=MIDDLE  ALT=\"C=1509.8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28t%29=%289.8%2F3%29%28t-e%5E%28t%29%29%2B1509.8%2F3 ALIGN=MIDDLE  ALT=\"x%28t%29=%289.8%2F3%29%28t-e%5E%28t%29%29%2B1509.8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );