PhysicsLAB CP Workbook
Vectors and the Parallelogram Rule

When vectors A and B are at an angle to each other, they add to produce the resultant C by the parallelogram rule. Note that C is the diagonal of a parallelogram where A and B are adjacent sides. Resultant C is shown in the first two diagrams, a and b.
 
      
 
Refer to the following information for the next two questions.

Construct the resultant C in diagrams c and d. Note that in diagram d you form a rectangle (a special case of a parallelogram). After you have finished your constructions, state in the blanks which resultant is the longer and which one is shorter.

                 
c. 

d. 

Refer to the following information for the next two questions.

Below we see a top view of an airplane being blown off course by wind in various directions. Use the parallelogram rule to show the resulting speed and direction of travel for each case.
        
In which case does the airplane travel fastest across the ground?
 
In which case does the airplane travel slowest across the ground?
 
Refer to the following information for the next three questions.

Below, on the right, we see top views of 3 motorboats crossing a river. All have the same speed relative to the water, and all experience the same water flow. Construct resultant vectors showing the speed and direction of the boats.
Which boat takes the shortest path to the opposite shore?
 
Which boat reaches the opposite shore first?
 
Which boat provides the fastest ride?
 




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