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 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

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 37.5

0 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

beneath any point on the dashed line is the same distance it would fall if dropped from rest!

5 m 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!

• End

Projectile Motion