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Chapter 3PROJECTILE 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
• An Airplane flying at 100 km/hr with a 20 km/hr wind
• With the wind 100 km/hr + 20 km/hr = 120 km/hr
• Against the wind • 100 km/hr - 20 km/hr = 80 km/hr
Velocity Vector EXAMPLE
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.
• Resolving a vector into its components
• Vertical
Component
Horizontal Component
Components of Vectors
PROJECTILE MOTION
• A falling object with constant linear velocity and vertical acceleration :
• Without gravity, a projectile launched upward would follow a straight line.
• The vertical distance a projectile falls beneath any point on the dashed line is the same distance it would fall if dropped from rest!
Upwardly Launched Projectiles
1 sec2 sec
3 sec
5 m
20 m45 m
IDEALPATH
ACTUAL PATH
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