Wide Down Under

November 19th, 2009 | Author: admin

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Wide Down Under

A power house, P, is on one bank of a straight river 200 m wide, and a factory, F, is on the opposite bank?

400 m down stream from P. The cable has to be taken across the river under water at a cost of $6/m. On land the cost is $3/m. What path should be chosen so that the cost is minimized?

Let's look at the extreme cases first:

Straight across the river is 200 m @ $6/m = $1200
plus 400 m on land @ $3/m = $1200, total $2400.

If we go diagonal, then by Pythagoras,
it's 200 sqrt(5) m @ $6/m = 1200 sqrt(5) ~= $2683

Let the point straight across from P be P'.
Let's choose a landfall point Q, somewhere P' and F.
Let distance from P' to Q be q.

So total distance is
sqrt (200² + q²) (diagonal under the river) + 400 - q (on land)
cost is 6 * sqrt(40000+q²) + 3 * (400 - q)
we want to minimize that.
first we can divide by 3 -- same value for q will be max
2 * sqrt(40000+q²) + 400 - q
Derivative is
2q / sqrt(40000+q²) - 1
We set that to 0
2q / sqrt(40000+q²) = 1
2q = sqrt(40000+q²)
Square:
4 q² = 40000 + q²
3 q² = 40000
q = 200/sqrt(3)

Length under water is then 400/sqrt(3) = approx 231
and length on land is 400 - 200/sqrt(3) = approx 284

Cost is 6 * 400/sqrt(3) + 3 (400 - 200/sqrt(3)) = 2239.23048

F
|
284
|
Q

|.
|..
q..231 (diagonal), q = 116
|.....
|......
P'.....P
..200..

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Rated: PG13Synopsis: Easily the most satisfying big-screen adventure film to star episodic-TV favorite Tom Selleck, Quigley Down Under rates kudos for its clever juxtaposition of horse-opera conventions and archetypes with an exquisite location and an unfamiliar but recognizable culture. Selleck plays a sharp-shooting westerner -- clad in typical cowboy regalia -- who travels to 19th-century Australia in response to an ad from British land baron Alan Rickman. The Yank, horrified to learn that he's been engaged to kill Aborigines as part of Rickman's campaign of native genocide, refuses his commission and thus becomes the target of the ruthless rancher's vendetta. Laura San Giacomo (who herself achieved small-screen stardom in the decade following this movie's production) is hardly a typical ingénue -- a trollop who is believed to be insane, she repeatedly confuses Selleck for a former lover. Wringing the rugged Australian landscape for every drop of pictorial splendor, director Simon Wincer (The Phantom) also exhibits a keen understanding of the morality-play elements that comprise classic movie westerns. His action scenes are vigorous and flamboyant, and his characters display markedly individualistic traits while behaving within the genre's long-prescribed limits. Exciting, picturesque, and occasionally very funny, Quigley Down Under will guarantee you a rip-roarin' good time. The DVD is augmented by a featurette, "Rebirth of a Western," in addition to the theatrical trailer. Tom Selleck stars as American cowboy archetype Matthew Quigley in Simon Wincer's outback western Quigley Down Under. Answering an advertisement placed by Australian cattle baron Elliot Marston (Alan Rickman) to come to the rugged and uncivilized Australian countryside and shoot dingoes, Quigley finds himself halfway around the world, only to find that Marston wants to exploit his talents as a sharpshooter in order to wipe out the Aborigine population. Taken aback by this square-jawed genocide, Quigley grabs Marston and hurls him through a window. Marston, who controls the region, sets out to hunt Quigley down. But helping him stay one step ahead of Marston is the addlebrained expatriate American trollop Crazy Cora (Laura San Giacomo) who insists that Quigley is her husband Roy. Paul BrennerVarietySelleck has his best bigscreen casting so far here (not counting the missed opportunity to be Indiana Jones). He's thoroughly convincing with his custom-made rifle and low-key manner. San Giacomo comes into her own as the feisty heroine. Rickman is a perfectly cast hissable villain. PRODUCTION AND TECHNICAL NOTES:Aspect Ratio: Cinemascope (2.35:1)Presentation: Wide ScreenSound: Dolby DigitalFeatures: Featurette: The Rebirth of a Western; original TV spots; original theatrical trailerLanguage: English, Français, EspañolSubTitles: English, Français, EspañolTime: 2 Hours