P H Y S I C S  

Chapter 2: Two-Dimensional Motion

Section 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

agni

tude

Angle = Directionθ

Adding Vectors

Rules: added in any order moved maintaining orientation added tip-to-tail

3 m east

4 m

nor

th

Res

ulta

nt =

5 m

NE

Adding Vectors

Which of the following is the correct orientation for adding these two vectors?

WRON

G

WRON

GRIG

HT

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