SOLUTION: Vector J has a magnitude of 28 ft and a direction of 34 degrees west of north. Vector K has a magnitude of 48 ft and a direction of 20 degrees south of east. Find the magnitude and

Question 864224: Vector J has a magnitude of 28 ft and a direction of 34 degrees west of north. Vector K has a magnitude of 48 ft and a direction of 20 degrees south of east. Find the magnitude and direction of their sum.
a) 30 ft and 13 degrees north of east
b) 36 ft and 54 degrees north of east
c) 38 ft and 27 degrees south of west
d) 40 ft and 14 degrees south of west
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Vector J has a magnitude of 28 ft and a direction of
34 degrees west of north = 90+34 = 124 degrees
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Vector K has a magnitude of 48 ft and a direction of
20 degrees south of east. = 340 degrees
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Find the magnitude and direction of their sum.
x-coordinate:: 28cos(124) + 48cos(340) = 29.45
y-coordinate:: 28sin(124) + 48sin(340) = 6.80
-------------------------
Ans:
Magnitude:: sqrt[29.45^2+6.80^2] = 30 ft
angle:: arctan(6.80/29.45) = 13 degrees
Ans: a
==============================================
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a) 30 ft and 13 degrees north of east
b) 36 ft and 54 degrees north of east
c) 38 ft and 27 degrees south of west
d) 40 ft and 14 degrees south of west

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