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55_Physics ProblemsTechnical Physics

55_Physics ProblemsTechnical Physics - 56 Vectors Q3.10 Any...

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56 Vectors Q3.10 Any vector that points along a line at 45° to the x and y axes has components equal in magnitude. Q3.11 A B x x = and A B y y = . Q3.12 Addition of a vector to a scalar is not defined. Think of apples and oranges. Q3.13 One difficulty arises in determining the individual components. The relationships between a vector and its components such as A A x = cos θ , are based on right-triangle trigonometry. Another problem would be in determining the magnitude or the direction of a vector from its components. Again, A A A x y = + 2 2 only holds true if the two component vectors, A x and A y , are perpendicular. Q3.14 If the direction of a vector is specified by giving the angle of the vector measured clockwise from the positive y -axis, then the x -component of the vector is equal to the sine of the angle multiplied by the magnitude of the vector. SOLUTIONS TO PROBLEMS Section 3.1 Coordinate Systems P3.1 x r = = °=
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