Chapter 3
PROJECTILE MOTION
How does a cannonball fly?
Or:
Did you realize that gravity and
wind resistance effect things ?
• We’ve looked at LINEAR MOTION, or the
motion of objects moving in a straight line.
• Now we’ll look at NONLINEAR MOTION
or motion along curved paths !
When we throw a ball :
• There is a constant velocity horizontal
motion
• And there is an accelerated vertical
motion
• These components act
independently of each other
Vector and Scalar Quantities
• Vector quantities require both
magnitude and direction
• They are represented by arrows with a numerical value
amount attached.
• EXAMPLES of Vector Quantities:
Power
velocity
Force
acceleration
Electric Current
directed energies
Vector and Scalar Quantities
• Scalar quantities require magnitude ONLY
and have no direction component.
• They are represented by a numerical value and units alone.
• EXAMPLES of Scalar Quantities:
Mass (grams)
volume (ml, liters, cm3)
time (sec., min., hr.)
speed (m/sec)
Scalars can be added, subtracted, multiplied or divided like
ordinary numbers
(3 kg + 4 kg = 7 kg)
15 min
delay in a 60 min trip means the trip took 75 min.
VELOCITY VECTORS
• Represented by arrows.
• The length of the arrow, drawn to scale,
indicates the magnitude of the vector.
• The direction of the arrow indicates the
relative direction of the vector quantity.
•
•
Large quantity vector
Small quantity vector
Velocity Vector EXAMPLE
• An Airplane flying at 100 km/hr with a
km/hr wind
20
• With the wind
100
km/hr + 20 km/hr = 120 km/hr
• Against the wind
• 100 km/hr - 20 km/hr = 80 km/hr
So what happens when the plane
meets a crosswind?
• The resulting flight path is not straight, but
IS a result of both velocity vectors.
RESULTANT
20 km/hr
crosswind
100 km/hr direction
VECTOR ADDITION
• 3 Step Technique
• Finds the RESULTANT of a pair of component vectors
that are at right angles (perpendicular) to each other.
• 1. Draw the 2 vectors with their tails touching
• 2. Draw a parallel projection of each vector to form a
rectangle
• 3. Draw the diagonal from the point where the 2 tails are
touching
VECTOR ADDITION – Step 1
• 3
•
4
VECTOR ADDITION – Step 2
• 3
•
4
VECTOR ADDITION – Step 3
• 3
•
•
5
37.50
4
VECTOR ADDITION - Examples
• Follow the example and complete the
following vector addition exercises.
Component Vectors
• Sometimes vectors need to be changed
into an equivalent set of Component
vectors.
• The vector is RESOLVED into 2
component vectors that are perpendicular
to each other.
• Any vector can be resolved into horizontal
and vertical components.
Components of Vectors
• Resolving a vector into its components
• Vertical
Component
Horizontal Component
PROJECTILE MOTION
• A falling object with constant linear velocity
and vertical acceleration :
Upwardly Launched Projectiles
• Without gravity, a projectile launched upward would
follow a straight line.
IDEAL
PATH
• The vertical distance a projectile falls
beneath any point on the dashed
45 m
line is the same distance
20 m
it would fall if dropped
5m
from rest!
1 sec
2 sec
ACTUAL
PATH
3 sec
PROJECTILE MOTION
• Launch a projectile from high enough and
fast enough and it will fall around the curve
of the Earth.
• This is referred to as going into orbit and
becoming a satellite.
Velocity Vectors
• An object is thrown in a long arc.
•
The horizontal vector does not change
while the vertical vector changes due to
gravity!
Projectile Motion
• End