Person Walks in Different Directions
A person walks in the following pattern 3.1 km North, then
2.4 km West and finally 5.2 km South.
(i) Sketch the vector diagram that represents this motion.
(ii) How far the person will be from its initial point?
(iii) In what direction would a bird fly in a straight line
from the same starting point to the same final point?
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Answer:
We label the displacement vectors
A
,
B
, and
C
(and denote the result of their vector sum as
r
). We choose east as the
i
^
direction (+x direction) and north as the
j
^
direction
(+y direction). All distances are understood to be in kilometers.
(a) The vector diagram representing the motion is shown next:
A
=(3.1km)
j
^
B
=(−2.4km)
i
^
C
=(−5.2km)
j
^
(b) The final point is represented by
r
=
A
+
B
+
C
=(−2.4km)
i
^
+(−2.1km)
j
^
Whose magnitude is
∣
r
∣=
(−2.4km)
2
+(−2.1km)
2
≈3.2km
(c) There are two possibilities for the angle:
θ=tan
−1
(
−2.4km
−2.1km
)=41
0
or 221
0
solution
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