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Post by sedgehammer on Mar 16, 2009 20:30:20 GMT -6
I was going through some questions in my textbook in preparation for my university calculus midterm and I stumbled upon a question that got my juices going. Though the conditions and assumptions of this question are not realistic, it made for a good question. I'll give anyone who guesses the correct answer $20 , 20 fishing points. ;D
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Deleted
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Post by Deleted on Mar 17, 2009 22:02:26 GMT -6
The answer is 0 m/s. If that fish is diving straight down at 3 m/s, then by the time the boat has travelled 50 m (ie 25 seconds later, the fish is now 75 m stright down, 150 m behind the boat, and I have long since run out of line ;D Ken
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Post by Dale Martens on Mar 17, 2009 23:34:43 GMT -6
Sounds suspiciously like a related rate problem to me...
Haven't done one of those in 20+ years...
At the time in question, suppose x is the horizontal distance between the boat and the fish (150 m), y is the vertical distance between the boat and the fish (75m) and l is the length of line off the reel (Pythagoreus gives that as 167m):
x2 + y2 = l2
Differentiating (implicitly!!!) with respect to time:
2xdx/dt + 2ydy/dt = 2ldl/dt
dx/dt is the boat's velocity. dy/dt is the fish's velocity. Factoring out the 2's and substituing:
150(2) + 75(3) = 167 dl/dt
Solving:
dl/dt = 3.14 m/s
The line pays off the reel at 3.14 m/s.
Am I close? Geez, what does all that above really say about me?
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stephenjay
Moderator
"Fish are too valuable to only catch once" - Lee Wulff
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Post by stephenjay on Mar 18, 2009 7:20:28 GMT -6
Sorry, but it's going to cost you more than $20 for me to do your homework!
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Post by sedgehammer on Mar 18, 2009 11:11:54 GMT -6
Nicely done Dale. However the actual answer is 3.13 m/s, not 3.14 m/s ;D ;D ;D Funny to think that some of my former high school colleagues believed that people would never use pre-calculus, never mind calculus, once they were done with it in school. I was under the impression that after being out of school for 20+ years, that calculus would be a long forgotten practice. Thanks for denying this common rumour. If I want to be an engineer I guess that would be a good thing to hang on to, even 20 years after school. Or else I might start doing crazy things like this... constructionfun.files.wordpress.com/2008/06/feat-of-engineering.jpg
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Post by sedgehammer on Mar 18, 2009 11:25:43 GMT -6
Nice try Ken, but that's the sort of answer you would receive a 0 for on a math test. Hopefully you knew this back in the day. Or else you would be receiving a lot of
'########## ##::::::::::::::: ######:::::::: ##::::::::::::::: ##:::::::::::::::
...and a lot of ;D stickers for "CLEVER, but no smart@$$ responses."
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Post by Dale Martens on Mar 18, 2009 23:12:56 GMT -6
Do I get part marks 'cause I showed my work?
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Deleted
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Post by Deleted on Mar 20, 2009 20:56:24 GMT -6
Nice try Ken, but that's the sort of answer you would receive a 0 for on a math test. Hopefully you knew this back in the day. Or else you would be receiving a lot of '########## ##::::::::::::::: ######:::::::: ##::::::::::::::: ##:::::::::::::::
...and a lot of ;D stickers for "CLEVER, but no smart@$$ responses." Phthtpththtpt! Doctors don't have to know math ;D ;D ;D Ken
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