2D Motion
Principles of Physics
CAR A
v = 2 m/s
CAR B
v=0
Both cars are the same distance above the ground, but Car A is traveling at 2 m/s
and Car B has no velocity. Which car will hit the ground first?
Assuming there is no friction, both will hit the ground at the same time!!!
Why do both cars hit the ground at the same time?
Only one force acts on them
GRAVITY
Gravity only acts up and down, so it only
affects the vertical motion of the object
 The horizontal motion of the object does
not affect vertical motion
How can an object have vertical and horizontal
motion at the same time??
Path if there
was no gravity
Path with combined
horizontal and
vertical motion
Path if object did
not have an initial
velocity
Projectiles
Objects under the influence of gravity ONLY
Examples
2D: objects with motion in both horizontal and
vertical directions
 Ball moving through the air after it has been thrown
 Clown shot out of a cannon at the circus
1D: objects in free fall or objects thrown straight upward
(only vertical motion)
 Skydiver (with no air resistance)
 Acorn falling from an oak tree
Trajectory
Path followed by a projectile
Horizontal: launched parallel to the ground
Angular: launched at an angle above the ground
θ
Horizontal Direction
 NO
forces act on the projectile
 Horizontal velocity is constant
Vertical Direction

Gravitational force acts on the object
 Object accelerates downward at 9.8 m/s2
 Velocity increases on the way down

Time the projectile is in the air depends on
how far down it falls
Problem Solving
vx
= horizontal velocity (m/s)
dx
= horizontal displacement (m)
t
= time (s)
dy
= vertical displacement (m)
a
= -9.8 m/s2
Problem Solving
x
d
vx  x
t
y
1 2
d y  at
2
Example 1: An object is thrown horizontally off a cliff with an
initial velocity of 5.0 m/s. The object strikes the ground 3.0 s
later. (Neglect Friction)
Calculate the horizontal displacement of the object.
x
dx
vx 
t
5=
dx __
3
dx = 15 m
y
dy 
1 2
gt
2
Example 1: An object is thrown horizontally off a cliff with
an initial velocity of 5.0 m/s. The object strikes the ground
3.0 s later. (Neglect Friction)
Calculate the vertical displacement of the object?
x
dx
vx 
t
y
1 2
d y  at
2
dy = ½ (9.8 ) (3)2
dy = 44.1 m
Example 2: A toy car drives horizontally with a velocity of 6
m/s off a table that is 1.6 m high. (Neglect friction)
Calculate the time it takes for the car to hit the ground.
x
y
1 2
d y  at
2
dx
vx 
t
1.6
= ½ (9.8) (t2)
1.6
4.9
= 4.9(t2)
4.9
0.33 = t2
t = 0.57 s
Example 2: A toy car drives horizontally with a velocity of 6
m/s off a table that is 1.6 m high. (Neglect friction)
Calculate the horizontal displacement of the object.
x
dx
vx 
t
6 =
dx __
0.57
dx = 3.42 m
y
dy 
1 2
gt
2