Projectile
Motion
Projectiles
z
Any object that moves through the air or
space, acted on only by gravity
– Near Earth, follow a curved path
– Can be broken down into two components.
z Vertical
z Horizontal
Horizontal Component
z
Like horizontal motion of a ball rolling
freely on a level surface
z Friction is negligible, rolling ball moves at a
constant velocity
z Ball covers = distance in = time intervals
z If no horizontal force acts on the ball, there
is not horizontal acceleration
z Same is true for projectiles.
“When no horizontal force acts
on a projectile, the horizontal
velocity remains constant.”
Vertical Component
z
Resembles that of free falling objects.
z Force due to gravity in vertical direction
z Projectile accelerated downwards
z Velocity changes with time
vf = at + vi
z Increased speed in vertical direction causes
greater distance to be covered with each
successive time interval
z
Horizontal Component TOTALLY
independent from vertical component.
z
Combined effects generate the curved paths
projectiles follow.
Horizontal + Vertical = Curved Path
Simultaneous Balls Dropped
z
z
z
One ball launched
horizontally
One ball simply
dropped
Analyze the path by
considering horizontal
and vertical
components separately
Horizontal
•Ball moves same horizontal
distance in = time intervals
•Happens because no
horizontal component of force
acts on it.
•The balls horizontal
component of motion remains
the same
Vertical
• Ball’s vertical
component of
motion remains the same
• Both balls fall the same
vertical distance in the
same time
9 Vertical distance
fallen has nothing to
do with horizontal
component of
acceleration
9 Downward motion of
horizontally
projected balls is the
same as free fall
z
We can use all our equations in both the x
and y directions SEPARATELY.
z
Ex: A ball rolls off a 1m table at 2m/s. How
far does it land form the table?
z
Path traced by a projectile accelerating only
in the vertical direction while moving at
constant horizontal velocity is called a
parabola.
z
Awesome so far Mr. Bolken. This is so
interesting.
z Can we do some practice problems?
z
Sure thing kids, here you go –
– Read Chapter 3 sections 1 & 2 on vectors
– Practice 3C: 1 &3 & 3D: 1-4
Upwardly Launched
Projectiles
z
z
Cannonball follows
curved path and hits
the ground because of
gravity.
If no gravity,
cannonball follows a
straight line path
shown by dotted line.
Because of Gravity…
z
Cannonball continually falls beneath
imaginary line until it hits ground
z Vertical distance it falls beneath any point
on dashed line is same vertical distance it
would fall if it dropped from rest and had
fallen for the same amount of time.
z Distance can be measured by
xf = ½ gt2 + vit + xi
z
Since there is no horizontal acceleration, the
cannonball moves = horizontal distances per
time interval.
Vectors
z
Vectors represent both
vertical and horizontal
components for a
projectile on a
parabolic path.
z Horizontal component
always the same
same magnitude/value
z
z
Resultant velocity
vector represented by
rectangle formed by
component parts.
Velocity at top of path
= horizontal
component because
vertical velocity is
zero
Projectiles Shot at Steeper
Angles
z
Initial velocity has greater vertical
component than when projectiles angle is
less
z Greater vertical component results in higher
path
z Horizontal component is less, therefore the
range is less
Things to Note
z
Same range
obtained for two
different projectile
angles – angles that
add up to 90
degrees.
z
z
Thrown at 60 degrees,
will land in the same
place as object thrown
at a 30 degree angle
with same speed.
Smaller angle remains
in air for shorter
amount of time.
Air Resistance
z
z
1)
2)
3)
If air resistance is not negligible, range of projectile is
smaller and path is not a true parabola.
If there is no air resistance…
Projectile rises to maximum height in some time in same
time it takes to fall from height to ground.
Deceleration due to gravity going up = acceleration due
to gravity coming down
Object hits ground at the same speed it had originally
left ground
Fast Moving Objects
z
z
If an object were
thrown so fast that is
clears the horizon, it
would then orbit the
Earth and become an
Earth Satellite.
Earth Satellite –
projectile moving fast
enough to fall around
the earth rather than
into it.
THE END
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