Everything Science Grade 11

11.7 CHAPTER 11. VECTORS

The Head-to-Tail Method

In describing the mathematical properties of vectors we used displacements and the head-to-tail graph-
ical method of vector addition as an illustration.The head-to-tail methodof graphically adding vectors
is a standard method that must be understood.

Method: Head-to-Tail Method of Vector Addition

1. Draw a rough sketchof the situation.


2. Choose a scale and include a reference direction.


3. Choose any of the vectors and draw it as anarrow in the correct direction and of the correct
   length – remember to put an arrowhead on theend to denote its direction.


4. Take the next vectorand draw it as an arrowstarting from the arrowhead of the first vector inthe
   correct direction and ofthe correct length.


5. Continue until you have drawn each vector –each time starting fromthe head of the previous
   vector. In this way, the vectors to be added are drawn one after the otherhead-to-tail.


6. The resultant is thenthe vector drawn from the tail of the first vectorto the head of the last.Its
   magnitude can be determined from the length of its arrow using the scale. Its direction too can
   be determined from thescale diagram.

Example 2: Head-to-Tail AdditionI

QUESTION

A ship leaves harbour Hand sails 6 km north to port A. From here the shiptravels 12 km east to

port B, before sailing 5,5km south-west to port C. Determine the ship’s resultant displacement

using the head-to-tail technique of vector addition.

SOLUTION

Step 1 : Draw a rough sketch of the situation

Its easy to understand the problem if we first draw a quick sketch. The rough

sketch should include all of the information given in the problem. All of the

magnitudes of the displacements are shown and a compass has beenincluded

as a reference direction. In a rough sketch oneis interested in the approximate

shape of the vector diagram.

H

6 km

A

12 km

B

5,5 km

C

45 ◦

N

S

W E

Step 2 : Choose a scale and include a reference direction.