document.write( "Question 1184788: In a soccer match, a ball is kicked from the ground with an initial velocity of 96ft/s². The function for the projectile motion of the ball is H(t)=-16t²+96t. When will the ball reach its maximum height? What is the maximum height? \n" ); document.write( "
Algebra.Com's Answer #815424 by ikleyn(52866)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "In a soccer match, a ball is kicked from the ground with an initial velocity of 96ft/s².
\n" ); document.write( "The function for the projectile motion of the ball is H(t)=-16t²+96t.
\n" ); document.write( "When will the ball reach its maximum height? What is the maximum height?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "This quadratic function is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    h(t) = -16t^2 + 96t = -16t*(t-6).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It has zeroes (y-intercepts) t= 0 and t= 6.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The maximum of this quadratic function is reached half-way between the roots  t= 0 and t= 6,\r\n" );
document.write( "\r\n" );
document.write( "and this half-way point is t= 3 seconds.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It means that the ball reaches its maximum height at t= 3 seconds, and the maximum height is equal to\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    h(3) = -16*3^2 + 96*3 = -16*9 + 96*3 = 144.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The ball reaches the maximum height of 144 feet at the time t= 3 seconds.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved and thoroughly explained.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For better understanding,  see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Introductory lesson on a projectile thrown-shot-launched vertically up \r
\n" ); document.write( "\n" ); document.write( "    - Problem on a projectile moving vertically up and down\r
\n" ); document.write( "\n" ); document.write( "    - Problem on an arrow shot vertically upward\r
\n" ); document.write( "\n" ); document.write( "    - Problem on a ball thrown vertically up from the top of a tower \r
\n" ); document.write( "\n" ); document.write( "    - Problem on a toy rocket launched vertically up from a tall platform\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Consider these lessons as your textbook,  handbook,  tutorials and  (free of charge)  home teacher.
\n" ); document.write( "Read them attentively and learn how to solve this type of problems once and for all.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic \"Projectiles launched/thrown and moving vertically up and dawn\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );