The circumstance of you ending up at the starting point from taking steps A and B would be if you take
one step along A and another step that is the same length of A along direction B. However, two nonzero
vectors add up to zero only if the magnitude is equal and direction is opposite. Furthermore, the
maximum distance one can end up starting from A and B equal to the sum of the magnitude (A + B).
Problem/Exercise:
4. Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from
your starting point, and what is the compass direction of a line connecting your starting point to
your final position? (If you represent the two legs of the walk as vector displacements
A
and
B , as
in Figure 3.53, then this problem asks you to find their sum
R=A+B .)
30.8 m, 54.2º N of W
16. Solve the following problem using analytical techniques: Suppose you walk 18.0 m straight west
and then 25.0 m straight north. How far are you from your starting point, and what is the compass
direction of a line connecting your starting point to your final position? (If you represent the two

legs of the walk as vector displacements
A
and
B , as in Figure 3.58, then this problem asks you to
find their sum
R=A+B .)
A. 30.8 m
B. 54.2º N of W
18. You drive 7.50 km in a straight line in a direction 15º east of north. (a) Find the distances you
would have to drive straight east and then straight north to arrive at the same point. (This
determination is equivalent to find the components of the displacement along the east and north
directions.) (b) Show that you still arrive at the same point if the east and north legs are reversed in
order.
A.
East:
D
E
= 7.50 km
.
sin
(15º)
D
E
= 1.94 km
North: D
N
= 7.50 km
.
cos
(15º)
D
N
= 7.24 km
B. D
N
+ D
E
= D
E
+ D
N

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- Fall '19
- Jane Smith
- Acceleration, Velocity, 10.3 km, 0.846m, 0.676m, 7.24 km