CHAPTER 11. VECTORS 11.7
The man’s resultant displacement is the vector from where he startedto where
he ended. It is the vector sum of his two separate displacements. We will use the
head-to-tail method of accurate construction to find this vector.
Step 4 : Choose a suitable scale
A scale of 1 cm represents 10 m (1 cm = 10 m)is a good choice here. Now we
can begin the process of construction.
Step 5 : Draw the first vector toscale
We draw the first displacement as an arrow 4 cmlong in an eastwards direction.
4 cm = 40 m
N
S
W E
Step 6 : Draw the second vector to scale
Starting from the head of the first vector we drawthe second vector as anarrow
3 cm long in a northerlydirection.
4 cm = 40 m
3 cm = 30 m N
S
W E
Step 7 : Determine the resultant vector
Now we connect the starting point to the end point and measure the length and
direction of this arrow (the resultant).
5 cm = 50 m
4 cm = 40 m
3 cm = 30 m
?
N
S
W E
Step 8 : Find the direction
To find the direction youmeasure the angle between the resultant and the 40 m
vector. You should get about 37◦.
Step 9 : Apply the scale conversion
Finally we use the scaleto convert the length of the resultant in the scalediagram
to the actual magnitudeof the resultant displacement. According to thechosen
scale 1 cm = 10 m. Therefore 5 cm represents 50 m. The resultant displacement
is then 50 m 37◦north of east.
