ast?dep= 17067116 Two the location of the first team as 34 km away, 13° nor team

Question

ast?dep= 17067116 Two the location of the first team as 34 km away, 13° nor team as 22 km away, 30P east of north. When the first team uses its GPS to check the position of the second team, what does the GPS give for the following 1 37 from the first team, Vector A has a magnitude of 140 units and points 36.0 resultant vector that is zero. Using components, find the magnitudes of the following vectors nts 63.0 east of north, vector C points 11.0° west of south. These three vectors add to give a 125 8 units 173 99 Section 18 o 9

Explanation / Answer

1)34 km away, 13° north of west

22 km away, 39° east of north

Let x = 34 km ; y = 22 km

theta = 90 - 16 + 39 = 113 deg

Using the law of cosines

z^2 = x^2 + y^2 - 2 x y cos(theta)

z^2 = 34^2 + 22^2 - 2 x 34 x 22 x cos113 = 2224.53

z = sqrt(2224.53) = 47.16 km

Hence, z = 47.16 km

b)The angle can be calculated by law of sines

Sin(theta)/z = sinY/y

Y = sin^-1(y sin(theta)/z)

Y = sin^-1(22 x sin113/47.16) = 25.47 deg

angle = 25.47 - 13 = 12.47 deg North of East

Hence, alpha = 12.47 deg North of East.

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