document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=192340>Question 192340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having problems with this type of question\r<BR>\n" );
document.write( "\n" );
document.write( "Find the height, of a ball, above ground using the following information.\r<BR>\n" );
document.write( "\n" );
document.write( "wait 3 seconds, velocity is 45 ft/sec, initial height above ground is 10 ft<BR>\n" );
document.write( "wait 2 seconds, velocity is 95 ft/sec, initial height above ground is 50 ft </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144368 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=144368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This  is  a  physics  problem  under  \"projectile  motion\"\r<BR>\n" );
document.write( "\n" );
document.write( "Sometimes  it  is  found  in  algebra  under  quadratic  topics  as  a  actual  application  example.\r<BR>\n" );
document.write( "\n" );
document.write( "For  today,  we  are  asked  how  high  the  projectile  will  go,  in  a  given  time,  with  an  initial  velocity.    The  velocity  provides  the  upward  energy,  and  gravity  provides  the  downward  energy.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Usually,  the  angle  of  the  initial  velocity  is  important,  but  for  today  we  will  assume  straight  up.    \r<BR>\n" );
document.write( "\n" );
document.write( "If  not,  let  me  know.\r<BR>\n" );
document.write( "\n" );
document.write( "The  basic  eqn  is:\r<BR>\n" );
document.write( "\n" );
document.write( "delta  y  =  v*t - (1/2) (32.2)  t^2\r<BR>\n" );
document.write( "\n" );
document.write( "where : <BR>\n" );
document.write( "delta  y  is  change  in  height.  Note  as  time  progresses,  the  projectile  goes  up,  reaches  a  peak,  and  then  comes  down.  \r<BR>\n" );
document.write( "\n" );
document.write( "v  is  initial  velocity.   units  in  this  case  are    ft per  sec or  ft/sec\r<BR>\n" );
document.write( "\n" );
document.write( "t  is  elapsed  time.  units  are  sec\r<BR>\n" );
document.write( "\n" );
document.write( "32.2  is  gravity.  we  are  using  English  today.  be  careful  of  metric.  english  units  are  32.2  ft  per  sec  squared,  or  32.2  ft/sec^2     (metric  is  9.8  m/sec^2)\r<BR>\n" );
document.write( "\n" );
document.write( "1/2  is  a  constant  to  get  average  acceleration\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1st  problem\r<BR>\n" );
document.write( "\n" );
document.write( "y= vt-1/2 (32.2) t^2\r<BR>\n" );
document.write( "\n" );
document.write( "    = (45) (3) -  1/2 (32.2) (3^2)\r<BR>\n" );
document.write( "\n" );
document.write( "    =  135  - 144.9\r<BR>\n" );
document.write( "\n" );
document.write( "    =  (-9.9)  ft\r<BR>\n" );
document.write( "\n" );
document.write( "Note  we  started  at  10  ft  above  ground, therefore  10-9.9  =  (.1)  ft  above  ground\r<BR>\n" );
document.write( "\n" );
document.write( "This  is  not  so  nice  a  first  problem.  The  projectile  has  been  in  the  air  long  enough  to  go  fully  up,  stop,  and  now  decend  to  just  above  ground   height.  \r<BR>\n" );
document.write( "\n" );
document.write( "Additional  calc  shows  that  the  projectile  goes  up  to  a  peak  of  about  31.4  ft  in  1.4  sec  before  starting  down.\r<BR>\n" );
document.write( "\n" );
document.write( "2nd  problem\r<BR>\n" );
document.write( "\n" );
document.write( "y=vt-16.1t^2 =  95*2  -16.1 *  2^2=  190-64.4=125.6  ft\r<BR>\n" );
document.write( "\n" );
document.write( "Again,  initial  height  was  50  ft,  therefore  final  position  is  50+125.6 =175.6   ft\r<BR>\n" );
document.write( "\n" );
document.write( "additional  calc  shows  peak  at  about  3 sec  of  about  140 ft<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );