Chapter 3Chapter 3

Projectile Projectile MotionMotion

3.1 Vector and Scalar Quantities3.1 Vector and Scalar Quantities

VECTOR QUANTITIESVECTOR QUANTITIES – – quantities that have quantities that have magnitude and directionmagnitude and direction

EX: force and velocityEX: force and velocity

3.1 Vector and Scalar 3.1 Vector and Scalar QuantitiesQuantities

SCALAR QUANTITIESSCALAR QUANTITIES – –

quantities that have quantities that have magnitude, but no directionmagnitude, but no direction

EX: mass, volume, timeEX: mass, volume, time

MAGNITUDE – strength of MAGNITUDE – strength of somethingsomething

“ “how much?”how much?”

DIRECTION – DIRECTION –

“ “which way?”which way?”

3.2 Vectors3.2 Vectors

vectorvector – represented by an – represented by an arrow whose length is the arrow whose length is the magnitude of a physical magnitude of a physical entity and whose entity and whose orientation shows how the orientation shows how the physical entity is directed.physical entity is directed.

MAGNITUDEMAGNITUDE

less magnitudeless magnitude

more more magnitudemagnitude

DIRECTIONDIRECTION

EQUAL MAGNITUDE; EQUAL MAGNITUDE; OPPOSITE DIRECTIONOPPOSITE DIRECTION

SPEED VS. VELOCITYSPEED VS. VELOCITY

Velocity has both magnitude Velocity has both magnitude and direction.and direction.

Speed has only magnitude.Speed has only magnitude.

You can add the You can add the magnitudes of two magnitudes of two vectors together to get vectors together to get the magnitude of the the magnitude of the resultantresultant vector. vector.

RESULTANTRESULTANT

the sum of two or more the sum of two or more vectorsvectors

(and takes into account (and takes into account their directions)their directions)

For Example:For Example:

100 m/s +100 m/s +200 m/s200 m/s

300 m/s net 300 m/s net velocity velocity

or resultant or resultant velocityvelocity

Also:Also:100 m/s +100 m/s +200 m/s200 m/s

100 m/s net 100 m/s net velocityvelocity

or resultant or resultant velocityvelocity

For example:For example:

100 km/hr

10 km/hr

Net Velocity:

90 km/hr

OROR

100 km/hr

10 km/hr

Net Velocity:

110 km/hr

WIND

Not all vectors occur Not all vectors occur horizontally.horizontally.

Say the wind was blowing at the Say the wind was blowing at the plane from the side.plane from the side.

WIND

The plane’s velocity is affected The plane’s velocity is affected by the wind.by the wind.

Plane’s velocity

Crosswind velocity

The plane’s resultant vector The plane’s resultant vector would look something like this:would look something like this:

By using the parallelogram By using the parallelogram method, you can represent method, you can represent the resultant of two vectors.the resultant of two vectors.

Geometric Addition of Geometric Addition of VectorsVectors

ParallelogramsParallelograms – shapes – shapes that have opposite sides that have opposite sides of equal length and are of equal length and are parallel.parallel.

EXAMPLES of parallelogramsEXAMPLES of parallelograms

Create a parallelogram from Create a parallelogram from the two vectors --the two vectors --

then connect the corners. then connect the corners. The diagonal is the resultant The diagonal is the resultant

vector.vector.

Special Case:Special Case:

If you have a 90 degree If you have a 90 degree angle, you can use the angle, you can use the Pythagorean Theorem to Pythagorean Theorem to calculate the magnitude of calculate the magnitude of the resultant.the resultant.

PYTHAGOREAM PYTHAGOREAM THEOREMTHEOREM

AA22 + B + B22 = C = C22

side A

side B

C (hypotenuse)

For example:For example:

332 + 42 = C2

9 + 16 = C2

4

?

25 = C2

C = 25 C = 5

SOH CAH TOASOH CAH TOA

–Sine Sine = opposite/hypotenuse = opposite/hypotenuse–Cosine Cosine = adjacent/hypotenuse = adjacent/hypotenuse–Tangent Tangent = opposite/adjacent = opposite/adjacent

–You can use these when you are You can use these when you are missing the lengths of any of the missing the lengths of any of the components.components.

3.3 Components of Vectors3.3 Components of Vectors

COMPONENTCOMPONENT – one of the – one of the vectors in a horizontal or vectors in a horizontal or vertical direction whose vertical direction whose vector sum is equal to the vector sum is equal to the given vector.given vector.

3.3 Components of 3.3 Components of VectorsVectors

ResolutionResolution – the – the process of determining process of determining the components of a the components of a given vectorgiven vector

X and Y are components (vectors)

V is the vector that is resolved

X

YV

Vector V has components X & Y

X

YV

3.4 Projectile Motion3.4 Projectile Motion

ProjectileProjectile – any object that is – any object that is launched by some means and launched by some means and continues in motion by its own continues in motion by its own inertiainertia

EX: a cannonball shot from a cannon EX: a cannonball shot from a cannon a stone thrown in the aira stone thrown in the air

a ball rolling off the tablea ball rolling off the table

GravityGravity

Gravity acts DOWNWARDGravity acts DOWNWARD

A ball moving horizontally is immune A ball moving horizontally is immune

to the effects of GRAVITY on its to the effects of GRAVITY on its velocity.velocity.

There is no vertical component, only a There is no vertical component, only a horizontal component.horizontal component.

GravityGravity

The instant ball is dropped, The instant ball is dropped, gravity acts on it, gravity acts on it,

pulling it toward the pulling it toward the center of the earth.center of the earth.

Now it only has a Now it only has a vertical component.vertical component.

3.5 Upwardly-Moving 3.5 Upwardly-Moving ProjectilesProjectiles

Figure 3.10Figure 3.10

If a projectile had no gravity If a projectile had no gravity acting on it, it would move with acting on it, it would move with this path:this path:

Gravity changes the path of Gravity changes the path of the projectile:the projectile:

Gravity pulls the projectile Gravity pulls the projectile

towards the Earth.towards the Earth.

Pathways of ProjectilesPathways of Projectiles

Objects that move at a Objects that move at a constant horizontal velocity constant horizontal velocity while being accelerated while being accelerated vertically down, take a path vertically down, take a path called a PARABOLA.called a PARABOLA.

PARABOLAPARABOLA

At each point in its path the At each point in its path the projectile has velocity vectors such projectile has velocity vectors such

as those below:as those below:

Each velocity vector has a vertical Each velocity vector has a vertical and a horizontal component.and a horizontal component.

Acceleration is constant for a Acceleration is constant for a projectile.projectile.

Speed and velocity change at each Speed and velocity change at each point along the parabolic point along the parabolic pathway.pathway.

What is the speed of the projectile What is the speed of the projectile at the very top of its pathway?at the very top of its pathway?

What is the acceleration of the What is the acceleration of the projectile at the very top of its projectile at the very top of its pathway?pathway?

Air ResistanceAir Resistance

Air resistance is another force that Air resistance is another force that acts on projectiles.acts on projectiles.

It changes the path of a projectile It changes the path of a projectile like this:like this:

Air ResistanceAir Resistance

IDEAL PATH

ACTUAL PATH

Air ResistanceAir Resistance

If air resistance is If air resistance is negligible, a projectile will negligible, a projectile will rise to its maximum height rise to its maximum height in the same amount of time in the same amount of time it takes it to fall back down.it takes it to fall back down.

Air ResistanceAir Resistance

Without air resistance, the Without air resistance, the deceleration of the deceleration of the projectile going up is equal projectile going up is equal to the acceleration of the to the acceleration of the projectile coming back projectile coming back down.down.

3.6 Fast-Moving Projectiles:3.6 Fast-Moving Projectiles:SatellitesSatellites

SatelliteSatellite – an object that falls – an object that falls around Earth or some other around Earth or some other body because of its body because of its tremendous speed, instead of tremendous speed, instead of falling into it.falling into it.–Page 201Page 201

Chapter 3 Key TermsChapter 3 Key Terms

ComponentComponentProjectileProjectileResolutionResolutionResultantResultant

SatelliteSatelliteScalar Scalar

quantityquantityVectorVectorVector Vector

quantityquantity