document.write( "Question 221662: Hi, I am having trouble with a word problem. The problem states \"When a rock is dropped from a cliff into an ocean, it travels approximately 16t^2 ft in t seconds. If the splash is heard 4.5 seconds later and the speed of sounds is 1100ft/sec, approximate the height of the cliff.\"\r
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Algebra.Com's Answer #166247 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
When a rock is dropped from a cliff into an ocean, it travels approximately 16t^2 ft in t seconds.
\n" ); document.write( "If the splash is heard 4.5 seconds later and the speed of sounds is 1100ft/sec, approximate the height of the cliff.\"
\n" ); document.write( ":
\n" ); document.write( "t = time for the rock to reach the water
\n" ); document.write( "then
\n" ); document.write( "(4.5-t) = time for the sound to reach the top of the cliff
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\n" ); document.write( "Both the rock and the sound will travel the same distance.
\n" ); document.write( "Write a distance equation
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\n" ); document.write( "16t^2 = 1100(4.5-t)
\n" ); document.write( "16t^2 = 4950 - 1100t
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\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( "16t^2 + 1100t - 4950 = 0
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\n" ); document.write( "Simplify, divide by 2
\n" ); document.write( "8t^2 + 550t - 2475
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\n" ); document.write( "Use the quadratic formula to find t:
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "in this problem x=t; a=8; b=550; c=-2475
\n" ); document.write( "\"t+=+%28-550+%2B-+sqrt%28+550%5E2+-+4+%2A+8+%2A-2475+%29%29%2F%282%2A8%29+\"
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\n" ); document.write( "\"t+=+%28-550+%2B-+sqrt%28302500+-+%28-72900%29+%29%29%2F%2816%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"t+=+%28-550+%2B-+sqrt%28302500++%2B+72900+%29%29%2F%2816%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"t+=+%28-550+%2B-+sqrt%28381700+%29%29%2F%2816%29+\"
\n" ); document.write( "we only want the positive solution here
\n" ); document.write( "\"t+=+%28-550+%2B+617.819%29%2F16+\"
\n" ); document.write( "t = \"67.819%2F16\"
\n" ); document.write( "t = 4.239 sec for the rock to hit the water
\n" ); document.write( "and
\n" ); document.write( "4.5 - 4.238 = .261 sec for the sound to come back
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\n" ); document.write( "You can use either value to find the height of the cliff
\n" ); document.write( "16(4.238^2) = 287 ft
\n" ); document.write( "and
\n" ); document.write( "1100(.261) = 287 ft
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\n" ); document.write( "Make sense to you?
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