document.write( "Question 1182042: The stream of water from a fountain follows a parabolic path, modeled by the function
\n" ); document.write( "f(x) = -1/4x^2 + 6x + 3, where x is the time elapsed in seconds, and h(x) is the height in feet. \r
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Algebra.Com's Answer #812006 by ikleyn(52778) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "As I see from the post, the person who created this problem (the problem's composer) is INFAMILIAR with\r
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\n" ); document.write( "\n" ); document.write( "The given function   b(x) = -(1/4)x^2 + 6x + 3,   where x is time, in seconds, and b(x) is the height of the stream in feet,\r
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\n" ); document.write( "\n" ); document.write( "        The problems on a projectile thrown-shot-launched vertically up are very popular.\r
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\n" ); document.write( "\n" ); document.write( "        READ it and LEARN it before create your problems and/or post them to this forum.\r
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document.write( "If you have the formula for a height given to you as a function of time in the form\r\n" );
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document.write( "    h(t) = -at^2 + bt + c,    (1)\r\n" );
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document.write( "where \"a\", \"b\" and \"c\" are real numbers, a > 0, then in this formula\r\n" );
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document.write( "    (a)  the initial height is equal to the coefficient \"c\" value;\r\n" );
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document.write( "    (b)  the initial velocity is the coefficient  \"b\" in the formula;\r\n" );
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document.write( "    (c)  the coefficient \"a\" value is half of the gravity acceleration.\r\n" );
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document.write( "         For the Earth conditions, the gravity acceleration is g = 32 ft/s^2,\r\n" );
document.write( "         if you use feet for height;\r\n" );
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document.write( "         So, in this case  a =  = 16  (numerical value).\r\n" );
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document.write( "    (d)  To find the height at the time moment \"t\", simply substitute the value of \"t\" into the formula (1) and calculate.\r\n" );
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document.write( "    (e)  To find the time \"t\" when the height has a given value h = , substitute  h =  into equation (1)\r\n" );
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document.write( "         and solve equation  \r\n" );
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document.write( "             h(t) = -at^2 + bt + c = .    (2)\r\n" );
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document.write( "    (f)  To find the time when the height is maximal, use the formula\r\n" );
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document.write( "              = .      (3)\r\n" );
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document.write( "    (g)  To find the maximal height, substitute the time value  t=   of the formula (3)  into the formula (1).\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see numerous examples of solved problems, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Problem on a projectile moving vertically up and down\r
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\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( "    - OVERVIEW of lessons on a projectile thrown/shot/launched vertically up\r
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