document.write( "Question 1185880: An object is thrown upward from a height of 80 ft. The initial velocity of the object is 64 ft per second. If the height h (in feet) is h=-16 +64t+80, where t is time in seconds, when will the object reach the ground? \n" ); document.write( "

Algebra.Com's Answer #816775 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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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( "            But, as I often observed, the students who meet such problems for the first time, often write \r
\n" ); document.write( "\n" ); document.write( "            the basic equation incorrectly, because they do not understand the meaning of its terms.\r
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\n" ); document.write( "\n" ); document.write( "            Therefore, I wrote this introductory lesson specially for beginners who don't know the subject AT ALL.\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( "What's all you need to know.\r
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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
\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( "    - OVERVIEW of lessons on a projectile thrown/shot/launched vertically up\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Use this file/link ALGEBRA-I - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-I.\r
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