document.write( "Question 101961: A rock is thrown upward at an initial velocity of 16 ft/sec from a height of 96 feet above ground. How long will it take to hit ground? \n" ); document.write( "
Algebra.Com's Answer #74168 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
The equation you are looking for is:
\n" ); document.write( ".
\n" ); document.write( "\"H+=+-16t%5E2+%2B+V%5Bo%5Dt+%2B+H%5Bo%5D\"
\n" ); document.write( ".
\n" ); document.write( "where the variables are defined as follows:
\n" ); document.write( ".
\n" ); document.write( "\"H\" is the height of the rock at time \"t\" after it is launched
\n" ); document.write( "\"t\" is the time after launch
\n" ); document.write( "\"V%5Bo%5D\" is the velocity with which the rock is launched
\n" ); document.write( "\"H%5Bo%5D\" is the height above the ground from which the rock is launched.
\n" ); document.write( ".
\n" ); document.write( "First \"V%5Bo%5D\" is given in the problem +16 ft/sec. The sign of this term is plus because the
\n" ); document.write( "rock is thrown upward. Next \"H%5Bo%5D\" is given in the problem as +96 ft. The sign of this
\n" ); document.write( "term is plus because the launch point is above the ground level. Substituting these two
\n" ); document.write( "values into the equation results in:
\n" ); document.write( ".
\n" ); document.write( "\"H+=+-16t%5E2+%2B+16t+%2B+96\"
\n" ); document.write( ".
\n" ); document.write( "One more thing. When the rock finally hits the ground, its height above the ground will
\n" ); document.write( "be zero. Therefore, substitute 0 as the value of H to make the equation:
\n" ); document.write( ".
\n" ); document.write( "\"0+=+-16t%5E2+%2B+16t+%2B+96\"
\n" ); document.write( ".
\n" ); document.write( "From here on, this is just a math exercise of solving a quadratic equation.
\n" ); document.write( ".
\n" ); document.write( "Note that 16 is a factor of every term on the right side ... therefore, you can divide both
\n" ); document.write( "sides of this equation (all terms) by 16 and the result is:
\n" ); document.write( ".
\n" ); document.write( "\"0+=+-t%5E2+%2B+t+%2B+6\"
\n" ); document.write( ".
\n" ); document.write( "To get this in a little more standard form, transpose the equation by switching sides, and
\n" ); document.write( "then multiply the entire equation by -1. When you do that you get:
\n" ); document.write( ".
\n" ); document.write( "\"t%5E2+-+t+-+6+=+0\"
\n" ); document.write( ".
\n" ); document.write( "This can be factored to:
\n" ); document.write( ".
\n" ); document.write( "\"%28t+-+3%29%2A%28t+%2B+2%29+=+0\"
\n" ); document.write( ".
\n" ); document.write( "Notice that this equation will be true if either of the factors is zero because multiplication
\n" ); document.write( "by zero on the left side will make the left side equal to the 0 on the right side.
\n" ); document.write( ".
\n" ); document.write( "So we can find the two possible answers for t by setting each of the factors equal to zero
\n" ); document.write( "to get:
\n" ); document.write( ".
\n" ); document.write( "\"t+-+3+=+0\"
\n" ); document.write( ".
\n" ); document.write( "and
\n" ); document.write( ".
\n" ); document.write( "\"t+%2B+2+=+0\"
\n" ); document.write( ".
\n" ); document.write( "The first is solved by adding 3 to both sides to get \"t+=+3\". The second is solved by
\n" ); document.write( "subtracting 2 from both sides to get \"t+=+-2\". This second solution can be ignored because
\n" ); document.write( "a minus value of time means a time before launch. The answer, therefore, is t = 3 seconds.
\n" ); document.write( "That means that 3 seconds after the launch of the rock (with an initial upward velocity of
\n" ); document.write( "16 ft/sec from a height of 96 ft) the rock will hit the ground.
\n" ); document.write( ".
\n" ); document.write( "Hope this helps you to understand how to set up the problem and then how to solve it.
\n" ); document.write( ". \n" ); document.write( "
\n" );