document.write( "Question 1093131: A bullet is shot straight up into the air from ground level. It reaches a maximum height at h= 821m.\r
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Algebra.Com's Answer #707731 by ikleyn(52748)\"\" \"About 
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document.write( "Apply the energy conservation law:\r\n" );
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document.write( "\"%28mv%5E2%29%2F2\" = mgH,\r\n" );
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document.write( "where m is the mass of the body, v is its initial vertical speed (m/s),\r\n" );
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document.write( "g is the gravity acceleration (9.81 m/s^2), H is the maximal height.\r\n" );
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document.write( "Canceling m in both sides and simplifying, you get\r\n" );
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document.write( "\"v%5E2\" = 2gH,   or   v =  = 126.9 m/s.\r\n" );
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document.write( "By knowing the initial speed, the physicist momentarily will find the time to reach the maximum height\r\n" );
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document.write( "t = \"v%2Fg\" = \"126.9%2F9.81\" = 12.9 seconds.\r\n" );
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document.write( "and the total time to get the ground is twice of this, i.e. 25.8 seconds.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solution 2     (School math)\r
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document.write( "Your expression for the height above the ground as a function of time is this quadratic function \r\n" );
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document.write( "h(t) = \"-4.9%2At%5E2+%2B+v%2At\".\r\n" );
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document.write( "The maximum is achieved at  t = \"-b%2F%282a%29\" = \"-v%2F%28-2%2A4.9%29\" = \"v%2F9.8\"    and is equal to\r\n" );
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document.write( "H = \"-4.9%2A%28v%2F9.8%29%5E2+%2B+v%2A%28v%2F9.8%29\" = \"%28-4.9%2F9.8%29%2A%28v%5E2%2F9.8%29+%2B+%28v%5E2%2F9.8%29\" = \"%28-1%2F2%29%2A%28v%5E2%2F9.8%29+%2B+%28v%5E2%2F9.8%29\" = \"%281%2F2%29%2A%28v%5E2%2F9.8%29\".\r\n" );
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document.write( "So, you obtain practically the same equation \r\n" );
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document.write( "H = \"%281%2F2%29%2A%28v%5E2%2F9.8%29\",   or   \"v%5E2\" = 2*9.8*H,   or   \"v\" = \"sqrt%282%2A9.8%2AH%29\" = \"sqrt%282%2A9.8%2A821%29\" = 126.9 m/s,\r\n" );
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document.write( "and the same answer for vertical speed.\r\n" );
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\n" ); document.write( "To wider your horizon and to get a solid base regarding problems on projectile launched vertically up,  see 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
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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( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I\r
\n" ); document.write( "\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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