Page 33 - Schaum's Outline of Theory and Problems of Applied Physics
P. 33

18                                      VECTORS                                   [CHAP. 2











                                                  Fig. 2-2











                                                  Fig. 2-3

        resultant R is the vector drawn from the tail of the first vector to the head of the last. The order in which the
        vectors are added does not matter (Fig. 2-3).


        SOLVED PROBLEM 2.1
              A woman walks eastward for 5 km and then northward for 10 km. How far is she from her starting point?
              If she had walked directly to her destination, in what direction would she have headed?
                  From Fig. 2-4, the length of the resultant vector R corresponds to a distance of 11.2 km, and a protractor shows
                              ◦
              that its direction is 27 east of north.

















                                                     Fig. 2-4



        SOLVED PROBLEM 2.2
              Two tugboats are towing a ship. Each exerts a force of 6 tons, and the angle between the towropes is 60 .
                                                                                               ◦
              What is the resultant force on the ship?
                  To add the force vectors A and B, vector B is shifted parallel to itself so that its tail is at the head of A. The
              length of the resultant R corresponds to a force of 10.4 tons. (See Fig. 2-5.)


        SOLVED PROBLEM 2.3
              A boat moving at 5 km/h is to cross a river in which the current is flowing at 3 km/h. In what direction
              should the boat head to reach a point on the other bank of the river directly opposite its starting point?
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