document.write( "Question 1180942: A projectile is fired at an angle of 30 degrees above the horizontal from the top of a cliff 600 ft high. The initial speed of the projectile is 2000 ft/s. How far will the projectile move horizontally before it hits the level ground at the base of the cliff? \n" ); document.write( "

Algebra.Com's Answer #810776 by ikleyn(52858) $\"\"$ $\"About$

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\n" ); document.write( "A projectile is fired at an angle of 30 degrees above the horizontal from the top of a cliff 600 ft high.
\n" ); document.write( "The initial speed of the projectile is 2000 ft/s. How far will the projectile move horizontally
\n" ); document.write( "before it hits the level ground at the base of the cliff?
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document.write( "Vertical component of the initial velocity is half of 2000 ft/s, or 1000 ft/s.\r\n" );
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document.write( "Therefore, the equation for the verical coordinate h(t) is\r\n" );
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document.write( "    h(t) = -16t^2 + 1000t + 600\r\n" );
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document.write( "The equation to find the time of the flight is  h(t) = 0,  or\r\n" );
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document.write( "    -16t^2 + 1000t + 600 = 0,  or\r\n" );
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document.write( "     4t^2 - 250t - 150 = 0.\r\n" );
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document.write( "Its roots are   =  =  = .\r\n" );
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document.write( "Of these two roots, only positive is interesting for us  t =  = 62.8 seconds  (rounded).\r\n" );
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document.write( "The horizontal component of the speed is   = 1732 ft/s (rouned) and is considered as a constant during the flight.\r\n" );
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document.write( "Moving with the horizontal speed of 1732 ft/s during 62.8 seconds, the projectile will get the ground at the distance of  \r\n" );
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document.write( "       62.8*1732 = 108769.6 feet from the cliff base.      ANSWER\r\n" );
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