document.write( "Question 1090435: A body travels half of its path length in last second of its free fall. Calculate the height from which it falls ? \n" ); document.write( "

Algebra.Com's Answer #705024 by ikleyn(52797) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A body travels half of its path length in last second of its free fall. Calculate the height from which it falls ?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "It is very well known fact from Physics, or from Calculus, or from your Algebra textbook, \r\n" );
document.write( "that a free falling body falls the distance (the height) \r\n" );
document.write( "\r\n" );
document.write( "H = \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "where t is the time of free falling counted from the very beginning time moment.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let us find the time t based on the given condition.\r\n" );
document.write( "\r\n" );
document.write( "Then your equation is \r\n" );
document.write( "\r\n" );
document.write( " -  = ,     or\r\n" );
document.write( "\r\n" );
document.write( " -  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now cancel the factor \"g\" in both sides. You will get the last equation in the form\r\n" );
document.write( "\r\n" );
document.write( " -  =     (*)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Since we excluded \"g\" from the equation, the solution for \"t\" does not depend on units we use \r\n" );
document.write( "    for the length or the distance (feet or meters).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify the equation (*)\r\n" );
document.write( "\r\n" );
document.write( " -  = ,\r\n" );
document.write( "\r\n" );
document.write( " = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The solution for t is  (use the quadratic formula)\r\n" );
document.write( "\r\n" );
document.write( " =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "By the meaning of the condition, the value of \"t\" must be greater than 1 second, so only the root  t =   makes sense.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the height under the question is\r\n" );
document.write( "\r\n" );
document.write( "H =  =  = 57.177 meters.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Check.  Notice that  =  = .\r\n" );
document.write( "\r\n" );
document.write( "        From the other side,   =  =  is exactly half of that.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you want to have the answer in feet, convert from meters to feet.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );