2 Dimensional
motion
Relativity of Velocity
Theory, developed in the early 20th
century, which originally attempted to
account for certain anomalies in the
concept of relative motion, but which in its
ramifications has developed into one of
the most important basic concepts in
physical science
Velocity changes when compared to a
frame of reference
Velocity can broken down into 2
dimensions.
– The vertical (free-fall acceleration)
– The horizontal (constant velocity)
Types of Acceleration
Acceleration , also known as linear
acceleration, rate at which the velocity
of an object changes per unit of time.
A = Dv/t (Average Acceleration)
Uniform Acceleration : the constant
rate of change in Velocity ( Free Fall )
– 9.81 m/s2 (use 10 m/s2 in multiple choice)
Vertical And Horizontal
Components
Horizontal and Vertical
components of motion are
independent.
A Cannon is fired
Horizontally from cliff
View this from two reference
frames:
1. Reference frame moving
across.
2. Reference frame on the
ground.
Vertical and Horizontal
Components #2
A ball is projected straight upwards by a
launcher located in the bed of the truck
the ball follows a parabolic
path and remains directly
above the launcher at all
times
As the ball rises towards its
peak, it undergoes a
downward acceleration
In the absence of horizontal
forces, there would be a
constant velocity in the
horizontal direction
Vertical and Horizontal
Components #3
The Monkey and Zookeeper feeding with a cannon
The banana moves in a
parabolic path in the
presence of gravity
The monkey also
accelerates downward once
he lets go of the limb.
Both banana and monkey
experience the same
acceleration since gravity
causes all objects to
accelerate at the same rate
regardless of their mass
Formulas
How to choose the best formula
•Free Fall
•Acceleration due
to gravity
•Uniform
acceleration
•Distance is not
part of the question
•Time is part of the
question
How to choose the best formula
•Free Fall
•Acceleration due to gravity
•Uniform acceleration
•Distance is part of the question
•Time is part of the question
How to choose the best formula
Choose this formula when the
question does not include the TIME
Sample Problem #1
A brick falls freely from a high
scaffold at a construction site.


What is the velocity after 4 seconds?
How far does the brick fall in this time?
Solution
Given: a = 10 m/s2 t = 4s
What is the velocity
after 4 seconds? Find: V
Vf = 0 m/s + (-10.0 m/s2) ( 4.0 s)
= -40 m/s
How far does the
brick fall in this
time? Find: d
d = 0 m/s (4s) + .5(-10.0 m/s2) (4s)2
= 0 + .5(-10.0m/s2) (16 s2 )
= -80m
Sample problem #2
An airplane must reach a speed of
71m/s for takeoff. If the runway is
1000m long, what must be the
acceleration?
Solution
What is the acceleration needed to
take off?
Given:
Vi=0 m/s
Vf=71 m/s
(71m/s)2
Find: a =?
d=1000m
= (0 m/s)2 + 2 (a) ( 1000m)
(-2000m) a = - 5041 m2 / s2
a = 2.5 m/s
2
Sample Problem #3
Melanie rolls a .010 kg
marble down a ramp
and off the table with
a horizontal velocity of
1.2 m/s. The marble
falls into a cup placed
0.51 m from the
table’s edge.
How high is the table?
Solution to Problem #3 part 1
Given: dx=0.51m Vx=1.2 m/s
Find: dy=?
Need to find t=?
Formula v=d/t
1.2 m/s = 0.51m/t
t = 0.51m / 1.2 m/s
t = 0.43 s
Solution to Problem #3 part 2
Given: dx=0.51m Vx=1.2 m/s
Find: dy=?
Found t=.43s
Formula dy= 1/2 g t2
dy= 1/2 (10m/s2) (0.43s)2
dy= (5m/s2) (0.1849)
dy= 0.92 m
Summary
Determine the type of motion
List the given information
Choose the best formula from the
Physics formulas
Substitute the proper units
Solve for the unknown in the
equation