Find the resultant of these two vectors....?

Find the resultant of these two vectors: 2.00 multiplied by 10 squared units due east and 4.00 multiplied by 10 squared units 30.0 degrees north of west..





A) 546 units, 59.3 degrees north of west


B) 300 units, 29.8 degrees north of west


C) 581 units, 20.1 degrees north of east


D) 248 units, 53.9 degrees north of west

Find the resultant of these two vectors....?
Answer is D)





Vector 1)


X = 200 (East)


Y = 0





Vector 2)


X = - 400 Cos(30 degrees) = - 346.4 (West is (-) )


Y = 400 Sin(30 degrees) = 200





Resultant Vector


X= 200 - 346.4 = -146.4 (West - )


Y = 0 + 200 = 200 (North)





Pythagorean Thereom:


Magnitude of Result Vector = (146.4^2 + 200^2) ^ 0.5


= 248





Only D) has 248 as magnitude. The Vector is moving slightly more North than West, so 53.9 degrees North of West makes intuitive sense.
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