Can you guys help me with probelm 46? Vector a has a magnitude of 5.0 m and is d

Question

Can you guys help me with probelm 46?

Vector a has a magnitude of 5.0 m and is directed cast. Vector b has a magnitude of 4.0m and is directed 36 degree west of due north. What are (a) the magnitude and (b)the direction off + b? What are (c) the magnitude and (d) the direction of b - a (e) Draw a vector diagram for each combination. Vectors A and B lie in an xy plane. A has magnitude 8.00 and angle 130 degree B has components B_x = -7.72 and = -9.20. What arc the angles between the negative direction of the y axis and (a) the direction of A. (b) the direction of he product and (c) the direction

Explanation / Answer

given are

vector a = 5.0 i

vector b = - 4*sin35 i + 4*cos35 j = - 2.3 i + 3.27 j

vector a + b = 5.0 i - 2.3 i + 3.27 j = 2.7 i + 3.27 j

magnitude of a + b = sqrt (2.7^2 + 3.27^2) = 4.24 m

direction = arctan(3.27/2.7) = 50.45 deg north of east

vector b - a = - 2.3 i + 3.27 j - 5 i = - 7.3 i + 3.27 j

magnitude of b - a = sqrt (7.3^2 + 3.27^2) = 8 m

direction = arctan(3.27/(-7.3)) = - 24.12 deg

direction is 24.12 deg north of west

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