Ch 3 part 2: Projectile Motion and Vectors in 2...

Ch 3 part 2: Projectile Motion and Vectors in 2 dimensions
Projectile Motion
In studying more general motion of objects
moving through the air, we consider 2
dimensions (horizontal and vertical) together,
yet independent, to create curved paths.
 Although air resistance is important, it will be
most often ignored.
 Projectiles will be studied as they move freely
in the air under the influence of gravity alone.
(at g=9.80m/s2 downward)
Horizontal vs Vertical motion
Galileo first showed that horizontal and
vertical components of motion can be
studied separately.
 Notice the vertical
positions of each
ball in the picture.
Horizontal direction of motion
In the horizontal direction there is no acceleration
(ignoring air resistance) so the horizontal
component of velocity, vx remains constant and
equal to its initial value, vx0
 Horizontal displacement is given by
x = vx0 t
 An object projected horizontally will reach the
ground in the same time as an object dropped
vertically from same h.
Vertical direction of motion
Objects leaving their support and falling,
experience acceleration downward
instantly due to earth’s gravity,
a=g=9.80m/s2 near earth’s surface.
 Vy is initially zero, but experiences
continual increase until it hits the ground.
 If we consider y positive upward, then
ay = -g and from v=v0 +at, we get vy = -gt
since vy0 = 0. Vertical displacement is
given as y = -½ gt2 .
Illustrations of Projectiles
Notice horizontal and vertical
displacements here.
What happens to each
component over time?
What would you get if you combined
Horizontal and vertical displacement or
Velocity components with Pythagorean
Instantaneous velocity!
Projectiles launched at angles
For projectiles launched at some angle
into the air above the horizontal, only the
y component of velocity experiences
acceleration. Therefore it will decrease
on the way up, come to zero at the top,
and increase on the way down.
 The horizontal component of the initial
velocity remains constant throughout the
 Can a projectile like this ever land
“straight down”?