document.write( "Question 1182633: A 1.0 kg rocket dropped from a height of 6.0 m at what height is the rock's genetic energy twice is potential energy \n" ); document.write( "

Algebra.Com's Answer #812772 by ikleyn(52873) $\"\"$ $\"About$

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\n" ); document.write( "A 1.0 kg rocket dropped from a height of 6.0 m at what height is the rock's genetic energy twice is potential energy
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\n" ); document.write( "\n" ); document.write( "            For the person, who calls kinetic energy as \"genetic energy\" and misses \"rocket\" with \"rock\", \r
\n" ); document.write( "\n" ); document.write( "            I would NEVER write any solution. He (or she) does not deserve it . . . \r
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\n" ); document.write( "\n" ); document.write( "            But I think about other people and next generations students, who will read my post in the future.\r
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\n" ); document.write( "\n" ); document.write( "I will start re-formulating the problem as it should sound.\r
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document.write( "    A 1.0 kg rock dropped from a height of 6.0 m.\r\n" );
document.write( "    At what height is the rock's kinetic energy twice its potential energy ?\r\n" );
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document.write( "In the figure on the right I show a vertical trajectory of the falling rock.                   *     6 meters\r\n" );
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document.write( "The intial height is 6 m above the ground level.  The current position of the falling rock     Y\r\n" );
document.write( "is \"z\" meters above the ground level.                                                          |\r\n" );
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document.write( "                                                                                               - z\r\n" );
document.write( "In this current position, the kinetic energy is twice the body's potential energy.             |\r\n" );
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document.write( "We should find this current coordinate \"z\".                                                  ------- ground level\r\n" );
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document.write( "Due to the Mechanical Energy Conservation law, the kinetic energy of the rock in its current \r\n" );
document.write( "position  \"z\"  is equal to the loss of its potential energy from the height of 6 m to the current level  \"z\"\r\n" );
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document.write( "    kinetic energy (z) = loss of the potential energy = mg*(6-z)  joules.\r\n" );
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document.write( "The potential energy of the rock at the level  \"z\"  is  mgz  joules.\r\n" );
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document.write( "So, the equation to find z is\r\n" );
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document.write( "    mg*(6-z) = 2mgz,\r\n" );
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document.write( "where m is the mass of the body and g is the gravity acceleration.\r\n" );
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document.write( "Canceling the common factor mg in both sides of the last equation, we get\r\n" );
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document.write( "    6 - z = 2z.\r\n" );
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document.write( "We simplify this equation\r\n" );
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document.write( "    6 = 2z + z,   or  6 = 3z,\r\n" );
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document.write( "and find finally\r\n" );
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document.write( "    z = 2 meters.\r\n" );
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document.write( "ANSWER.  At the height of 2 meters above the ground level, the kinetic energy of the rock is twice its potential energy.\r\n" );
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