Chapter 3 Review
Chapter Summary
3.1. Kinematics in Two Dimensions: An Introduction

Observe that motion in two dimensions consists of horizontal and vertical
components.

Understand the independence of horizontal and vertical vectors in two-dimensional
motion.
3.2. Vector Addition and Subtraction: Graphical Methods

Understand the rules of vector addition, subtraction, and multiplication.

Apply graphical methods of vector addition and subtraction to determine the
displacement of moving objects.
3.3. Vector Addition and Subtraction: Analytical Methods

Understand the rules of vector addition and subtraction using analytical methods.

Apply analytical methods to determine vertical and horizontal component vectors.

Apply analytical methods to determine the magnitude and direction of a resultant
vector.
3.4. Projectile Motion

Identify and explain the properties of a projectile, such as acceleration due to
gravity, range, maximum height, and trajectory.

Determine the location and velocity of a projectile at different points in its
trajectory.

Apply the principle of independence of motion to solve projectile motion problems.
3.5. Addition of Velocities

Apply principles of vector addition to determine relative velocity.

Explain the significance of the observer in the measurement of velocity.
Key Equations
Equations of Motion
1
x = x0 + v0t + at2
2
vavg =
Free Fall:
v2 = vo2 + 2a(x-x0)
v = v0 + at
y=
Symmetric Projectiles:
x  x0
t
1 2
gt
2
H=
a=
v = gt
(vo sin o )2
2g
v  v0
t
(a = g
y0 = 0
vy0 = 0)
2vo2 sin o cos o
vo2 sin2 o
R=
=
g
g
T=
2vo sin o
g
v=
vx2  v y2
R = vxT
Vectors:
1 km = 1000m
vx = v cos 
vy = v sin 
1 m = 100 cm
 = tan-1
1 y = 3.16 x 107 s
1 h = 3600 s
vy
vx
g = 9.80 m/s2
Multiple Choice

Adding vectors with the head-to-tail method

Maximum and minimum value when adding two vectors together

Finding the magnitude of a vector given its components

Finding the angle a vector makes with respect to the +x axis given its components

Knowing the x- and y-components of a vector given its magnitude and direction

Comparison of speeds at different points in the trajectory of any projectile

Angles for maximum range and equal range

What happens to the range and height of a symmetric projectile when you double,
triple, etc. the initial velocity
Problems

Using the kinematic equations to find position of a horizontal, symmetric or
asymmetric projectile

Finding range, height and flight time of a horizontal, symmetric or asymmetric
projectile

Addition of vectors (i.e. boat or plane problems)

Problems similar to practice problems
Example Multiple Choice Problems
1. Which diagram below illustrates this relationship?
A) 1
B) 2
  
AB  C
C) 3
D) 4
2. A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the
magnitude of the resultant is:
A) 0
B) 1
C) 3
D) 5
E) 7
3. A vector has a component of 10 m in the +x direction and a component of 10 m in the
+y direction. The magnitude of this vector is:
A) 0
B) 10
C) 14
D) 20
E) 200
4. A vector in the xy plane has an x component of 4 and a y component of 3. The angle it
makes with the positive x axis is:
A) 26
B) 37
C) 43
D) 59
E) 85
5. If  is the angle with respect to the positive axis, the x-component of the vector A is
given by
A) Acos 
B) Acos 
C) Asin  D) mg – Asin 
6. Given the diagram to the right, what is the y-component of
the vector?
A) 16 m/s
B) 14 m/s
C) 10 m/sD. 8 m/s
Answers to Example Problems
1. C
2. A
3. C
4. B
5. A
16 m/s
6. D
60o
Add these two vectors using your ruler, protractor and the parallelogram method on the
axes below, and determine the resultant.
A
B
 
In the space below, sketch the addition of A  B using the head-to-tail method.
Using the component method, add the two vectors below.
x-component
y-component
A = 10.0 m @ -40.0o
B = 6.5 m @ 70.0o
--------------Rx =
R=
Solution:
Rx = 9.88 m
Ry = -0.320 m
--------------Ry =
=
R = 9.9 m
 = -1.9o (358.1o)