document.write( "Question 180636: Height of a Projectile
\n" ); document.write( "A projectile is fired straight upward from ground level with an initial velocity of 128 feet per second. During what time period will its height be less that 128 feet?
\n" ); document.write( "Please help me with this. Thanks! \n" ); document.write( "
Algebra.Com's Answer #135429 by ankor@dixie-net.com(22740)\"\" \"About 
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A projectile is fired straight upward from ground level with an initial velocity of 128 feet per second. During what time period will its height be less that 128 feet?
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\n" ); document.write( "The equation we use for this:
\n" ); document.write( "h = -16t^2 + 128t
\n" ); document.write( "where h is the height (in feet) in t seconds, launched at 128 ft/sec
\n" ); document.write( ":
\n" ); document.write( "Find the t when the projectile reaches 128 ft
\n" ); document.write( "-16t^2 + 128t = 128
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\n" ); document.write( "-16t^2 + 128t - 128 = 0
\n" ); document.write( "Simplify and change the signs, divide equation by -16
\n" ); document.write( "t^2 - 8t + 8 = 0
\n" ); document.write( ":
\n" ); document.write( "Solve this using the quadratic formula
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "a=1, b=-8, c=8 (x = t)
\n" ); document.write( "\"t+=+%28-%28-8%29+%2B-+sqrt%28-8%5E2+-+4+%2A1%2A8+%29%29%2F%282%2A1%29+\"
\n" ); document.write( "\"t+=+%288+%2B-+sqrt%2864+-+32+%29%29%2F%282%29+\"
\n" ); document.write( "\"t+=+%288+%2B-+sqrt%2832+%29%29%2F%282%29+\"
\n" ); document.write( "Two solutions:
\n" ); document.write( "\"t+=+%288+-+5.654685%29%2F%282%29+\"
\n" ); document.write( "\"t+=+2.34315%2F2\"
\n" ); document.write( "t = 1.17 sec, passes 128 ft on the way up
\n" ); document.write( "and
\n" ); document.write( "\"t+=+%288+%2B+5.654685%29%2F%282%29+\"
\n" ); document.write( "\"t+=+13.654685%2F2\"
\n" ); document.write( "t = 6.828 sec, passes 128 ft on the way down
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\n" ); document.write( "Graphically it can be seen
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-4%2C+10%2C+-50%2C+275%2C+-16x%5E2%2B128x%29+\"
\n" ); document.write( "Find when it strikes the ground
\n" ); document.write( "-16t^2 + 128t = 0
\n" ); document.write( "Factor
\n" ); document.write( "-16t(t - 8) = 0
\n" ); document.write( "t = 0
\n" ); document.write( "and
\n" ); document.write( "t = 8 sec
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\n" ); document.write( "we can say it's less than 128 ft:
\n" ); document.write( "1.17sec - 0 = 1.17 sec
\n" ); document.write( "and
\n" ); document.write( "8 - 6.83 = 1.17 sec
\n" ); document.write( "for a total of 3.34 seconds
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\n" ); document.write( "Hope this makes sense to you. studying the graph will help. \n" ); document.write( "
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