document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199009>Question 1199009</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown upward from 3 meters above ground level with a velocity of 14 meters per second. When does the ball hit the ground? \r<BR>\n" );
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document.write( "Here's the explanation:\r<BR>\n" );
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document.write( "1. The height starts at 3 meters.\r<BR>\n" );
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document.write( "2. It travels at 14 meters pee second or 14(m/s).\r<BR>\n" );
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document.write( "In solution step 2 we are told that 14(m/s) = 14t, where t is in seconds.\r<BR>\n" );
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document.write( "Where did t come from? \r<BR>\n" );
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document.write( "3. Gravity pulls the ball down changing its position by about 5 meters per second squared.\r<BR>\n" );
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document.write( "Where did 5 meters per second squared come from? <BR>\n" );
document.write( "We are told that it is written like this -5t^2.\r<BR>\n" );
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document.write( "Where did the minus 5 come from?\r<BR>\n" );
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document.write( "We are further told that -5t^2 is simplified from -(1/2)at^2, where a = 9.8 m/(s^2).\r<BR>\n" );
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document.write( "Where did this value of a come from? \r<BR>\n" );
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document.write( "The equation created by the given information is h = 3 + 14t - 5t^2. \r<BR>\n" );
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document.write( "In my opinion, none of this is given in the given application.\r<BR>\n" );
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document.write( "You say?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832691 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832691\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "The STANDARD formula for the height of a projectile launched vertically up is \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.   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 = 9.81 m/s^2, or 32 ft/s^2.\r\n" );
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document.write( "         THEREFORE, if you use meters for height, you may use the approximate value of g = 10 m/s^2.\r\n" );
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document.write( "         So, in this case  a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%2F2 ALIGN=MIDDLE  ALT=\"g%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5  (the numerical value).\r\n" );
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document.write( "         ALTERNATIVELY, if you use feet for height, you should use the approximate value of g = 32 ft/s^2.\r\n" );
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document.write( "         So, in this case  a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%2F2 ALIGN=MIDDLE  ALT=\"g%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 16  (the 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 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D ALIGN=MIDDLE  ALT=\"h%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, substitute  h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D ALIGN=MIDDLE  ALT=\"h%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D ALIGN=MIDDLE  ALT=\"h%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.    (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( "             <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bmax%5D ALIGN=MIDDLE  ALT=\"t%5Bmax%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2F%282a%29 ALIGN=MIDDLE  ALT=\"b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.      (3)\r\n" );
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document.write( "    (g)  To find the maximal height, substitute the time value  t= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bmax%5D ALIGN=MIDDLE  ALT=\"t%5Bmax%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >  of the formula (3)  into the formula (1).\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "That's all you need to know.\r<BR>\n" );
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document.write( "---------------\r<BR>\n" );
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document.write( "To see numerous examples of solved problems, &nbsp;look into the lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/travel/Problem-on-a-projectile-moving-vertically.lesson>Problem on a projectile moving vertically up and down</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/travel/Problem-on-projectile-shooted-vertically-upward.lesson>Problem on an arrow shot vertically upward</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/travel/Typical-problems-on-an-projectile-moving-vertically-up-and-down.lesson>Problem on a ball thrown vertically up from the top of a tower</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/travel/Problem-on-a-toy-rocket-launched-vertically-up--from-the-top-of-a-platform.lesson>Problem on a toy rocket launched vertically up from a tall platform</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Consider these lessons as your textbook, &nbsp;handbook, &nbsp;tutorials and &nbsp;(free of charge) &nbsp;home teacher.<BR>\n" );
document.write( "Read them attentively and learn how to solve this type of problems once and for all.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this textbook under the topic \"<U>Projectiles launched/thrown and moving vertically up and dawn</U>\".\r<BR>\n" );
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document.write( "Save the link to this online textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-I<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "to your archive and use it when it is needed.\r<BR>\n" );
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document.write( "<U>Comment from student</U> : &nbsp;&nbsp;To find out when the ball will hit the ground, <BR>\n" );
document.write( "let h = 0 and solve for t. &nbsp;&nbsp;h = 3 + 14t - 5t^2. 0 = 3 + 14t - 5t^2. &nbsp;&nbsp;Yes?\r<BR>\n" );
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document.write( "<U>My response</U> : &nbsp;&nbsp;Yes. &nbsp;&nbsp;Correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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