Hello,
The question is the following: the resultant of two vectors, A and B, is a vector of 40 meters oriented towards the north. If the magnitude of A is 30 m and it forms an angle of 30 degrees towards the south in relation to the west, determine the vector of B. Thank you for your help.
Hello!
First, let's begin with drawing a vector diagram:
Since R is the result of vector sum of A and B (or algebraic sum of their components like AS and AW), and since R does not have neither W- nor E-component, we conclude that the horizontal component of B (BW or BW) must 'cancel' AW. It means that
Draw this vector:
Consider the vertical component of R. It is a result of subtracting the vertical component of A from the vertical component of B (because A points downward):
Draw it:
Therefore, according to Pythagorean theorem, we have
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