document.write( "Question 83099: A helicopter is taking off vertically when a crate slips out of the cargo door. At that instant, the helicopter is moving upward at 15 m/s and is 50 m above the ground. What is the maximum height the crate will reach above the ground?\r
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Algebra.Com's Answer #59753 by ankor@dixie-net.com(22740)\"\" \"About 
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A helicopter is taking off vertically when a crate slips out of the cargo door. At that instant, the helicopter is moving upward at 15 m/s and is 50 m above the ground. What is the maximum height the crate will reach above the ground?
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\n" ); document.write( "Using 1/2 the gravitational acceleration of a falling object; 9.8m/s^2:
\n" ); document.write( "h = -4.9x^2 + 15x + 50, where x = time in seconds
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\n" ); document.write( "Find the axis of symmetry using x = -b/(2a); in this problem a=-4.9, b=+15
\n" ); document.write( "x = -15/(2*-4.9)
\n" ); document.write( "x = -15/-9.8
\n" ); document.write( "x = +1.53 seconds
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\n" ); document.write( "Max height would be the vertex, find that, substitute 1.53 for x:
\n" ); document.write( "h = -4.9(1.53^2) + 15(1.53) + 50
\n" ); document.write( "h = -4.9(2.34) + 22.95 + 50
\n" ); document.write( "h = -11.47 + 22.95 + 50
\n" ); document.write( "h = 61.48 meters max height of the wayward box
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\n" ); document.write( "After falling from the helicopter, how long will the crate be in the air?
\n" ); document.write( "That will be when h = 0
\n" ); document.write( "-4.8x^2 + 15x + 50 = 0
\n" ); document.write( "Use the quadratic formula; a=-4.9, b=15, c=50
\n" ); document.write( "\"x+=+%28-15+%2B-+sqrt%28+15%5E2-+4+%2A+-4.9+%2A+50+%29%29%2F%282%2A-4.9%29+\"
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\n" ); document.write( "\"x+=+%28-15+%2B-+sqrt%28+225+-+%28-980%29%29%29%2F%28-9.8%29+\"
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\n" ); document.write( "\"x+=+%28-15+%2B-+sqrt%28+1205%29%29%2F%28-9.8%29+\"
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\n" ); document.write( "Do the math here you should get a positive solution of
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\n" ); document.write( "x = 5.1 seconds for it to hit the ground
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\n" ); document.write( "A graph of this:
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-2%2C+8%2C+-10%2C+70%2C+-4.9x%5E2+%2B+15x+%2B+50%29+\"
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\n" ); document.write( "Did this help?\r
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