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

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

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 sec 2 sec 3 sec 5 m 20 m 45 m IDEAL PATH 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