document.write( "Question 1153458: The height of a projectile launched upward at a speed of 32 feet/second from a height of 48 feet is given by the function: h(t)=-16t^2+32t+48. How long will it take the projectile to hit the ground? \n" ); document.write( "

Algebra.Com's Answer #775688 by ikleyn(52802) $\"\"$ $\"About$

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document.write( "Your basic equation is\r\n" );
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document.write( "    h(t) = -16t^2 + 32t + 48.\r\n" );
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document.write( "The projectile will hit the ground when h(t) = 0.\r\n" );
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document.write( "Thus the equation to solve is\r\n" );
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document.write( "    -16t^2 + 32t + 48 = 0.    (1)\r\n" );
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document.write( "You can simplify this equation SIGNIFICANTLY dividing both sides by -16. \r\n" );
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document.write( "You will get an EQUIVALENT equation\r\n" );
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document.write( "    t^2 - 2t - 3 = 0.    (2)\r\n" );
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document.write( "The term \"EQUIVALENT\" means that it has the same roots as equation (1).\r\n" );
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document.write( "Now you can factor equation (2) easily  (and MENTALLY)\r\n" );
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document.write( "    (t-3)*(t+1) = 0.\r\n" );
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document.write( "The roots are  t= 3  and  t= -1, and only  positive root t= 3 is meaningful.\r\n" );
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document.write( "ANSWER.  The projectile will hit the ground in 3 seconds.\r\n" );
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