Chapter 3 PROJECTILE MOTION How does a cannonball

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, cm 3) 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 • • 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 5 m 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