document.write( "Question 1105310: A ball is thrown from an initial height of 6 feet
\n" ); document.write( "with an initial upward velocity of 36 ft/s.
\n" ); document.write( "(a) After how many seconds did it hit the ground?
\n" ); document.write( "(b) After how many seconds did it reach its maximum
\n" ); document.write( "height?
\n" ); document.write( "(c) What was its maximum height? \n" ); document.write( "
Algebra.Com's Answer #720099 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
A ball is thrown from an initial height of 6 feet
\n" ); document.write( "with an initial upward velocity of 36 ft/s.
\n" ); document.write( "(a) After how many seconds did it hit the ground?
\n" ); document.write( "(b) After how many seconds did it reach its maximum
\n" ); document.write( "height?
\n" ); document.write( "(c) What was its maximum height?
\n" ); document.write( "
\r\n" );
document.write( "The formula is \r\n" );
document.write( "\r\n" );
document.write( "\"h%28t%29=h%5B0%5D%2Bv%5B0%5Dt-16t%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "where h0 = initial height = 6 feet\r\n" );
document.write( "where v0 = initial velocity (upward if positive) = 36 ft/s\r\n" );
document.write( "\r\n" );
document.write( "\"h%28t%29=6%2B36t-16t%5E2\"\r\n" );
document.write( "

\n" ); document.write( "(a) After how many seconds did it hit the ground?
\n" ); document.write( "
\r\n" );
document.write( "We set h(t) = 0 and solve for t\r\n" );
document.write( "\r\n" );
document.write( "\"0=6%2B36t-16t%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"16t%5E2-36t-6=0\"\r\n" );
document.write( "\r\n" );
document.write( "Divide through by 2\r\n" );
document.write( "\r\n" );
document.write( "\"8t%5E2-18t-3=0\"\r\n" );
document.write( "\r\n" );
document.write( "That doesn't factor, so we use the quadratic formula,\r\n" );
document.write( "and find it has only one feasible (positive solution, \r\n" );
document.write( "approximately 2.4 seconds later.\r\n" );
document.write( "

\n" ); document.write( "(b) After how many seconds did it reach its maximum
\n" ); document.write( "height?
\n" ); document.write( "
\r\n" );
document.write( "We use the vertex formula \"-b%2F%282a%29\"for the horizontal coordinate\r\n" );
document.write( "of the vertex:\r\n" );
document.write( "\r\n" );
document.write( "\"h%28t%29=6%2B36t-16t%5E2\"\r\n" );
document.write( "\"h%28t%29=-16t%5E2%2B36t%2B6\"\r\n" );
document.write( "\"a=-16\", \"b=36\",\r\n" );
document.write( "\r\n" );
document.write( "\"-b%2F%282a%29=-%2836%29%2F%282%28-16%29%29=%28-36%29%2F%28-32%29=9%2F8=1%261%2F8\" seconds.\r\n" );
document.write( "

\n" ); document.write( "(c) What was its maximum height?
\n" ); document.write( "
\r\n" );
document.write( "We substitute \"1%261%2F8\" seconds for t in\r\n" );
document.write( "\r\n" );
document.write( "\"h%28t%29=6%2B36t-16t%5E2\"\r\n" );
document.write( "\"h%281%261%2F8%29=6%2B36%281%261%2F8%29-16%281%261%2F8%29%5E2\"\r\n" );
document.write( "\"h%289%2F8%29=6%2B36%289%2F8%29-16%289%2F8%29%5E2\"\r\n" );
document.write( "\"h%289%2F8%29=26.25\" feet.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );