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Vectors X - component Y - componentA = 220 km, 10 0 N of W A X = A Y =B = 250 km, 45 0 W of N B X = B Y =C = 200 km, 50 0 N of E C X = C Y =D = 300 KM, 80 0 E of S D X = D Y =R X = R Y

Question

Vectors X - component Y - componentA = 220 km, 10 0 N of W A X = A Y =B = 250 km, 45 0 W of N B X = B Y =C = 200 km, 50 0 N of E C X = C Y =D = 300 KM, 80 0 E of S D X = D Y =R X = R Y

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Solution 1

It seems like you're asking for the X and Y components of vectors A, B, C, and D. Here's how you can calculate them:

  1. Vector A = 220 km, 10° N of W This means the vector is 10° north from the west direction. A_X = -220 cos(10°) = -217.47 km (West is considered negative in the X direction) A_Y = 220 sin(10°) = 38.23 km (North is considered positive in the Y direction)

  2. Vector B = 250 km, 45° W of N This means the vector is 45° west from the north direction. B_X = -250 cos(45°) = -176.78 km B_Y = 250 sin(45°) = 176.78 km

  3. Vector C = 200 km, 50° N of E This means the vector is 50° north from the east direction. C_X = 200 cos(50°) = 128.56 km C_Y = 200 sin(50°) = 153.21 km

  4. Vector D = 300 km, 80° E of S This means the vector is 80° east from the south direction. D_X = 300 cos(80°) = 52.33 km D_Y = -300 sin(80°) = -294.09 km (South is considered negative in the Y direction)

The resultant vector R can be found by adding the X and Y components of all vectors:

R_X = A_X + B_X + C_X + D_X R_Y = A_Y + B_Y + C_Y + D_Y

Please note that the above calculations assume that the angles are measured from the positive X-axis (East) in the counter-clockwise direction. If your convention is different, the calculations might need to be adjusted.

This problem has been solved

Solution 2

It seems like you're asking for the X and Y components of vectors A, B, C, and D. Here's how you can calculate them:

  1. Vector A = 220 km, 10° N of W This means the vector is 10° north from the west direction. A_X = -220 cos(10°) = -217.47 km (West is considered negative in the X direction) A_Y = 220 sin(10°) = 38.23 km

  2. Vector B = 250 km, 45° W of N This means the vector is 45° west from the north direction. B_X = -250 cos(45°) = -176.78 km B_Y = 250 sin(45°) = 176.78 km

  3. Vector C = 200 km, 50° N of E This means the vector is 50° north from the east direction. C_X = 200 cos(50°) = 128.56 km C_Y = 200 sin(50°) = 153.21 km

  4. Vector D = 300 km, 80° E of S This means the vector is 80° east from the south direction. D_X = 300 cos(80°) = 52.33 km D_Y = -300 sin(80°) = -294.09 km (South is considered negative in the Y direction)

The resultant vector R can be calculated by adding the X and Y components of all vectors:

R_X = A_X + B_X + C_X + D_X = -217.47 - 176.78 + 128.56 + 52.33 = -213.36 km R_Y = A_Y + B_Y + C_Y + D_Y = 38.23 + 176.78 + 153.21 - 294.09 = 74.13 km

So, the resultant vector R has an X component of -213.36 km and a Y component of 74.13 km.

This problem has been solved

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