document.write( "Question 827533: If a baseball is hit from home plate and leaves the ball park 330 feet from the home plate and is 16 feet from the ground and lands 390 feet from home plate. Find the maximum height of the ball and how many feet from home plate does it occur. \n" ); document.write( "

Algebra.Com's Answer #500068 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "We are missing how high the ball was above home plate when it was hit.\r\n" );
document.write( "I will arbitrarily assume that the ball was hit when it was 5 feet above \r\n" );
document.write( "the ground (home plate).  This is the graph.  The path of the ball is\r\n" );
document.write( "a parabola, and it goes through (0,5) when it is hit 5 feet above the\r\n" );
document.write( "ground.  It goes through (330,16), the point the ball is at when it leaves\r\n" );
document.write( "the park, and the point (390,0) when it hits the ground 390 feet from\r\n" );
document.write( "home plate.\r\n" );
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document.write( "A parabola has the general equation \r\n" );
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document.write( "y = Ax²+Bx+C\r\n" );
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document.write( "Substituting in point (0,5)\r\n" );
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document.write( "5 = A(0)²+B(0)+C\r\n" );
document.write( "5 = C\r\n" );
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document.write( "Substituting in point (330,16) and C=5\r\n" );
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document.write( "16 = A(330)²+B(330)+5\r\n" );
document.write( "16 = 330²A+330B+5\r\n" );
document.write( "11 = 330²A+330B\r\n" );
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document.write( "Divide through by 330\r\n" );
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document.write( "Substituting in point (390,0) and C=5 \r\n" );
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document.write( " 0 = A(390)²+B(390)+5\r\n" );
document.write( "-5 = 390²A+390B\r\n" );
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document.write( "Divide through by 390\r\n" );
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document.write( "Solve the system\r\n" );
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document.write( "Subtract the 1st equation from the 2nd\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "So the equation of the parabola is\r\n" );
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document.write( "To find the maximum height we use the vertex formula\r\n" );
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document.write( "The x-value of the vertex is given by \r\n" );
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document.write( " = 186.7\r\n" );
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document.write( "So the ball was 186.7 feet from home plate when it reached\r\n" );
document.write( "its maximum height.\r\n" );
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document.write( "We substitute that into\r\n" );
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document.write( "The vertex of the parabola is the point (186.7,31.808).\r\n" );
document.write( "So the maximum height of the ball was 31.808 feet and it occurred\r\n" );
document.write( "186.7 feet from home plate.\r\n" );
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document.write( "Now this was assuming that the ball was hit at a height of 5 feet\r\n" );
document.write( "above home plate.  If you are told another height, then you'll have\r\n" );
document.write( "to refigure it using that height.  Maybe your teacher meant for you\r\n" );
document.write( "to work it as though the ball was hit down on the ground.  That would\r\n" );
document.write( "change the answer slightly.  But the principle used above is correct.\r\n" );
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document.write( "Edwin

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