document.write( "Question 1170726: A player throws a ball straight up toward the roof of a gym. The height hin feet of the ball after tseconds can be modeled by the function h(t)=-16t^2+55t+4
\n" ); document.write( "a. The height of the gym roof is 53 feet. Will the ball hit the ceiling?
\n" ); document.write( "b. How long will it take for the ball to reach a height of 29 feet?
\n" ); document.write( "c. How high will the ball be 3 seconds after it’s thrown?
\n" ); document.write( "d. How high will be ball be 6.5 seconds after it’s thrown?
\n" ); document.write( "e. What is the maximum height the ball will reach?
\n" ); document.write( "f. How long will it take to reach that height? \n" ); document.write( "

Algebra.Com's Answer #795606 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "A player throws a ball straight up toward the roof of a gym. The height hin feet of the ball after t seconds
\n" ); document.write( "can be modeled by the function h(t)=-16t^2+55t+4
\n" ); document.write( "a. The height of the gym roof is 53 feet. Will the ball hit the ceiling?
\n" ); document.write( "b. How long will it take for the ball to reach a height of 29 feet?
\n" ); document.write( "c. How high will the ball be 3 seconds after it’s thrown?
\n" ); document.write( "d. How high will be ball be 6.5 seconds after it’s thrown?
\n" ); document.write( "e. What is the maximum height the ball will reach?
\n" ); document.write( "f. How long will it take to reach that height?
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\n" ); document.write( "\n" ); document.write( " I will place the questions and the answers in other, more natural order f), e), a), b), c) and d).\r
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document.write( "f.  How long will it take to reach the maximum height?\r\n" );
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document.write( "    It is about finding the maximum of the quadratic function  \r\n" );
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document.write( "        h(t) = -16t^2 + 55t + 4.     (1)\r\n" );
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document.write( "    Use the formula   = ,  where  \"a\"  is the coefficient at the quadratic term \r\n" );
document.write( "    and  \"b\"  is the coefficient at the linear term.\r\n" );
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document.write( "e.  What is the maximum height the ball will reach?\r\n" );
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document.write( "    Substitute the value of  ,  found in part f), into the formula (1).\r\n" );
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document.write( "    In this way, you will find the value of  .\r\n" );
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document.write( "a.  The height of the gym roof is 53 feet. Will the ball hit the ceiling?\r\n" );
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document.write( "    Compare the value of  , found in part e) above with the height of the celling of 53 ft.\r\n" );
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document.write( "b.  How long will it take for the ball to reach a height of 29 feet?\r\n" );
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document.write( "    To answer this question, solve the equation  -16t^2 + 55t + 4 = 29.\r\n" );
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document.write( "c.  How high will the ball be 3 seconds after it’s thrown?\r\n" );
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document.write( "    To answer this question, substitute the value of  t= 3 seconds into the formula (1).\r\n" );
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document.write( "d.  How high will be ball be 6.5 seconds after it’s thrown?\r\n" );
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document.write( "    To answer this question, substitute the value of  t= 6.5 seconds into the formula (1)\r\n" );
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document.write( "    If the result is greater than zero, then it is real height.\r\n" );
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document.write( "    If the result is negative, then the answer is h(t) = 0, which means \"the ball just reached the floor\".\r\n" );
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\n" ); document.write( "\n" ); document.write( "You are fully instructed now.\r
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\n" ); document.write( "\n" ); document.write( "If you want to see other similar problems solved, look into the lessons\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
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\n" ); document.write( "\n" ); document.write( "Consider these lessons as your textbook, handbook, tutorials, TEMPLATES, and/or (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
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\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
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\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
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\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
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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