A vector A has a magnitude of 40.0 m and points in a direction 20.0 degrees below the positive X-Axis. A second vector, B, has a magnitude of 60.0 m and points in a direction 50.0 degrees above the positive x axis. Find the magnitude and direction of A + B.
Not quite sure on how to start on this. A visual explanation would be greatly appreciated.
Not quite sure on how to start on this. A visual explanation would be greatly appreciated.
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For vector A:
X component = (40m)* [cos (360-20 degrees)] = 37.59m
Y component = (40m)* [sin (360 - 20 degrees)] = -13.68m
For vector B:
X component = (60m)*(cos 50 degrees) = 38.57m
Y component = (60m)*(sin 50 degrees) = 45.96m
For vector A + B:
X component = 37.59m+ 38.57m = 76.16m
Y component = -13.68m + 45.96m = 32.28m
Magnitude = (32.28m) / [sin (arc tan 32.28/76.16)] = 82.72m
Direction angle = arc tan (32.28/76.16) = 22.97 degrees
X component = (40m)* [cos (360-20 degrees)] = 37.59m
Y component = (40m)* [sin (360 - 20 degrees)] = -13.68m
For vector B:
X component = (60m)*(cos 50 degrees) = 38.57m
Y component = (60m)*(sin 50 degrees) = 45.96m
For vector A + B:
X component = 37.59m+ 38.57m = 76.16m
Y component = -13.68m + 45.96m = 32.28m
Magnitude = (32.28m) / [sin (arc tan 32.28/76.16)] = 82.72m
Direction angle = arc tan (32.28/76.16) = 22.97 degrees
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To sum vectors, you place the start of the second vector at the end of the first. Or you simply sum the x and y components of each vector after converting to cartesian.
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good luck.