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Word problem involving a vector ( Will rate lifesaver)

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Question:

Compute each scalar value to two decimal places and each angle to the nearest hundredth of a degree.

An airplane is flying in the direction N25degE with an airspeed of 450 kilometers per hour. It's ground speed of 500 kilometers per hour, and its course is N40degE.

Find:
a) The speed of the wind

b) The direction of the wind.

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Answers:

integral123

Apprentice

Karma Points: 180

Date Posted: 7/26/2008 5:27:24 AM Status: Live

Asker's Rating: Lifesaver

Response:

OA = 450 km/h, OB = 500 km/h, angle COA = 25 deg, angle COB = 40 deg,

AB - the speed of the wind, angle DCA gives its direction.

Part A:

Using cosine theorem, one can get the speed of the wind:

AB^2 = AO^2 + BO^2 - 2*AO*BO*cos AOB =

450^2 + 500^2 - 2*450*500*cos (40 - 25) = 1783 (km/h)^2

AB = 133.5 km/h

Part B:

From the same cosine theorem

cos OAB = (OA^2 + AB^2 - OB^2)/(2*OA*AB) =

(450^2 + 133.5^2 - 500^2)/(2*450*133.5) = -0.247

Angle OAB = 104.3 deg

Angle OAC = 180 - 104.3 = 75.7 deg

Angle OCA = 180 - OAC - COA = 180 - 75.7 - 25 = 79.3

And finally angle DCA = 180 - OCA = 100.7 deg

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Word problem involving a vector ( Will rate lifesaver)

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