P H Y S I C S
Chapter 2: Two-Dimensional MotionSection 2A: Adding and Resolving Vectors
Objectives:1) We differentiate a scalar and vector
2) We will add and resolve vectors
Scalar vs. Vector
Scalar only magnitude (numerical value)
Vector magnitude and direction
• Distance• Speed• Mass
• Temperature• Volume• Energy
• Density• Power• Work
• Displacement• Velocity• Acceleration
• Force• Momentum• Weight
Scalar or Vector
1) 75.2 degrees
2) 55 km west
3) 33.0 m/s @ 19.0o
4) 98.4 m
5) 8 m to the left
6) 14.0 cm
7) 16 km NW
8) 25 km/h
Scalar
Vector
Vector
Scalar
Vector
Scalar
Vector
Scalar
Vectors
Represented with an arrowLe
ngth
= M
agnit
ude
Angle = Directionθ
Adding Vectors
Rules: added in any order moved maintaining orientation added tip-to-tail
3 m east
4 m
nor
th
Result
ant =
5 m
NE
Adding Vectors
Which of the following is the correct orientation for adding these two vectors?
WRONG
WRONG
RIGHT
RIGHT
Adding Vectors
Resultant: Sum of two or more vectors
Magnitude
Direction
adjacent
oppo
site
hypo
tenu
se
θ
In-Class Example #1
Tom leaves home and drives 3 km north and then 5 km east to get to work. What is the total distance travelled and his total displacement?
∆x = 5.83 kmθ
xo
x
Projectile
Projectile: An object thrown/launched and curves due to gravity
Path: Trajectory Shape: Parabola
Which hits the ground first?
g g
Demo
Which hits the ground first?
Motion in the x and y directions are independent of each other
Projectile Motion x-dir motion not affected by gravity (y-dir)
Projectile Motion Gravity (y-dir) not affected by x-dir motion
Determining Hang Time of aHorizontally Launched Projectile
If projectile is horizontally launched then vi(y) = 0
Determine yi and yf
yo
y
Determining the Range of a Horizontally Launched Projectile
If projectile is horizontally launched all velocity vi is in x-dir vi = vi(x)
Determine time using y direction
vo = vo(x)
In-Class Problem #1
A marble rolls off a table that is 0.85 m high and lands 1.25 m from the base of the table.
a) How long was the marble in the air?b) What was the marble’s initial velocity?
t = 0.42 s vo = 2.98 m/s