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