Name
Period
Date
AP Physics Vectors Worksheet 2
Vector Addition
Computationally determine the resultants. Be sure each resultant has both a magnitude
and a direction.
1. You walk 15 m East , then 25 m at 30. North of East . What is your displacement?
a. Begin by sketching a vector diagram of the situation needed to find the resultant
displacement.
b. Sketch the perpendicular components for each vector shown below, and then
calculate these perpendicular components.
15 m
25 m
30.º
c. Calculate the perpendicular components of the resultant, sketch a new vector
diagram using these components, and then calculate the resultant displacement.
AP Vectors Worksheet 2
page 2
2. You are flying in a plane moving 150. m at 65 North of West, when a 40. m wind
s
s
begins to blow at 40. North of East . What is your resultant velocity?
a. Begin by sketching a vector
diagram of the situation needed
to find the resultant velocity.
b. Sketch the perpendicular components for each vector shown below, and then
calculate these perpendicular components.
40. m/s
40.º
150. m/s
65º
c. Calculate the perpendicular components of the resultant, sketch a new vector
diagram using these components, and then calculate the resultant velocity.
AP Vectors Worksheet 2

page 3

3. Velocities A and B are as shown.
Calculate both in unit vector notation
and in polar coordinates (magnitude
 
and direction) A  B .

A  15 m
y
40.o
20.o
x

B  9 .0 m
s
s
AP Vectors Worksheet 2
page 4
4. A particle undergoes three successive displacements in a plane as follows:
4.00 m due Southwest , 5.00 m East , and 6.00 m in a direction 60.0 North of East .
a. Find the magnitude and direction of the resultant displacement.
b. Find the displacement that would be required to bring the particle back to the
starting position.
AP Vectors Worksheet 2
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

5. Two displacements are given by a  4iˆ  3 ˆj  kˆ and b  iˆ  ˆj  4kˆ where both are in
meters. Find the following in unit vector notation.
 
a. a  b
 
b. a  b
  

c. A vector c such that a  b  c  0 .


6. Two displacements are given by a  4.0 m  iˆ  3.0 m  ˆj and b  6.0 m  iˆ  8.0 m  ˆj .
Find the magnitudes and directions of the following.

a. a

b. b
 
c. a  b
 
d. b  a
AP Vectors Worksheet 2
page 6
 
e. a  b
f. How do the orientations of (d) and (e) compare?
7. You walk 22 m South , then 15 m at 35 South of West , then 8.0 m at 20. South of
East. What is your displacement?