ch03-p010 - 10. We label the displacement vectors A , B and...

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10. We label the displacement vectors G A , G B and G C (and denote the result of their vector sum as G r ). We choose east as the ˆ i direction (+ x direction) and north as the ˆ j direction (+ y direction) All distances are understood to be in kilometers. (a) The vector diagram representing the motion is shown below: ˆ (3.1 km) j ˆ ( 2.4 km)i ˆ ( 5.2 km) j A B C = =− G G G (b) The final point is represented by ˆˆ ( 2.4 km)i ( 2.1 km)j rABC =++=− + GG G G whose magnitude is () 22 2.4 km 2.1 km 3.2 km r + G . (c) There are two possibilities for the angle: 1 2.1 km tan 41 ,or 221 2.4 km θ §· == ° ° ¨¸ ©¹ . We choose the latter possibility since
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