ch03-p019 - 19. Many of the operations are done efficiently...

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angle is –37.5°, which is to say that it is 37.5° clockwise from the + x axis. This is equivalent to 322.5° counterclockwise from + x . (c) We find ˆˆ ˆ ˆ [43.3 ( 48.3) 35.4] i [25 ( 12.9) ( 35.4)] j (127 i 2.60 j) m abc −+= −− + − −− +− = + G GG in unit-vector notation. The magnitude of this result is 22 2 | | (127 m) (2.6 m) 1.30 10 m. −+ = + × G (d) The angle between the vector described in part (c) and the + x axis is 1 tan (2.6 m/127 m) 1.2 ≈° . (e) Using unit-vector notation, G d is given by (4 0 . 4 i 4 7 . 4 j ) m dabc =+−=− + , which has a magnitude of ( 40.4 m) (47.4 m) 62 m. −+ = (f) The two possibilities presented by a simple calculation for the angle between the vector described in part (e) and the + x axis are 1 tan (47.4/( 40.4)) 50.0 −= ° , and 180 ( 50.0 ) 130 °+ − ° = ° . We choose the latter possibility as the correct one since it indicates that G d is in the second quadrant (indicated by the signs of its components). 19. Many of the operations are done efficiently on most modern graphical calculators
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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