Is this possible?Is this possible?

Explain your reasoningExplain your reasoning

Unit 3Unit 3

Projectile MotionProjectile Motion

ObjectivesObjectives LT3A- LT3A- RecognizeRecognize an object as a projectilean object as a projectile

LT3B- Predict the motion of a projectile launched horizontally in terms of LT3B- Predict the motion of a projectile launched horizontally in terms of the horizontal and vertical components of the motionthe horizontal and vertical components of the motionLT3C- Calculate the horizontal and vertical components of a vectorLT3C- Calculate the horizontal and vertical components of a vectorLT3D-Calculate the range, time of flight, initial velocity, and impact LT3D-Calculate the range, time of flight, initial velocity, and impact velocity of a projectile launched horizontallyvelocity of a projectile launched horizontallyLT3E- Predict the motion of a projectile at some angle in terms of the LT3E- Predict the motion of a projectile at some angle in terms of the horizontal and vertical components of the motionhorizontal and vertical components of the motionLT3F- Analyze and calculate horizontal and vertical components of a LT3F- Analyze and calculate horizontal and vertical components of a vector using trigonometric functionsvector using trigonometric functionsLT3G- Solve projectile motion problems representing the relationship LT3G- Solve projectile motion problems representing the relationship between projection angles, velocity, time of flight, range, and impact between projection angles, velocity, time of flight, range, and impact velocity.velocity.

Projectile MotionProjectile Motion A A projectileprojectile is any object that is projected is any object that is projected

by some means and continues in motion by some means and continues in motion by its own inertia.by its own inertia.

The The velocityvelocity of a projectile has a of a projectile has a horizontalhorizontal and and verticalvertical component. component.

Each component acts independentlyof the other!

Projectile MotionProjectile Motion Diagram and SymbolsDiagram and Symbols

VVi i = initial velocity= initial velocity

Range (dx)

height (dy) or ymax

Vy,i

vi

Vx,i

Vy,i = initial vertical velocity

Vx,i = initial horizontal velocity

Where do we see projectile Where do we see projectile motion?motion?

http://www.youtube.com/watch?http://www.youtube.com/watch?v=T9Kl6OtWZIc&feature=relmfuv=T9Kl6OtWZIc&feature=relmfu

http://www.youtube.com/watch?http://www.youtube.com/watch?v=WaIWJfqDkwY&NR=1&feature=fvwpv=WaIWJfqDkwY&NR=1&feature=fvwp

For the For the vertical motionvertical motion the acceleration is -the acceleration is -9.8m/s9.8m/s22 (or 9.8 m/ s (or 9.8 m/ s22 downward). downward).

For the horizontal motion there is NO acceleration.

Vy = Vi • sin

g = -9.8m/s2

Vy = Vi • cos

Vi

Vy

Vy

= launch angle(from the horizontal)

Projectile MotionProjectile MotionThe shape of a projectiles path is a The shape of a projectiles path is a

parabolaparabola..

Maximum rangeMaximum range for a projectile is for a projectile is achieved with a projection angle of 45°.achieved with a projection angle of 45°.

Does this theory hold?Does this theory hold?

At the instant a horizontally held rifle is fired, a At the instant a horizontally held rifle is fired, a bullet held at the rifle’s side is released and bullet held at the rifle’s side is released and drops to the ground. Which bullet strikes the drops to the ground. Which bullet strikes the ground first, the one fired from the rifle or the ground first, the one fired from the rifle or the one dropped?one dropped?

In the presence of In the presence of air resistanceair resistance, the , the trajectory of a high-speed projectile trajectory of a high-speed projectile falls short of a parabolic path.falls short of a parabolic path.

A projectile fired A projectile fired horizontallyhorizontally will hit the will hit the ground at ground at same timesame time as an object… as an object…

……dropped from rest if they are dropped from rest if they are released at the same height.released at the same height.

Demo:Demo: Ball projection and drop Ball projection and drop

What do you think?What do you think?

http://www.youtube.com/watch?http://www.youtube.com/watch?v=D9wQVIEdKh8&feature=relatedv=D9wQVIEdKh8&feature=related

Horizontal Motion and FreefallHorizontal Motion and FreefallThe ball’s horizontal component remains constant. B/c there is no horizontal force acting on it.

Once in flight the only force on the ball is gravity working in the vertical direction.

Both balls fall the same vertical distance in the same time. Vertical distance has nothing to do with Horizontal component of motion.

Downward motion of projected ball is the same as that of free fall.

Horizontal MotionHorizontal Motion GreenGreen: Absence of gravity, : Absence of gravity,

constant velocityconstant velocity

BlueBlue: Free fall: Free fall

RedRed: Horizontal projection in : Horizontal projection in presence of gravity, horizontal vel. presence of gravity, horizontal vel. Is not altered. Distance and time Is not altered. Distance and time are the same.are the same.

The vertical force acts perpendicular to the horizontal motion and will not affect it since perpendicular components of motion are independent of each other. Thus, the projectile travels with a constant horizontal velocity and a downward vertical acceleration.

Example QuestionExample Question If the snowmobile is in motion

and launches the flare and maintains a constant horizontal velocity after the launch, then where will the flare land (neglect air resistance)?

a. in front of the snowmobile b. behind the snowmobile c. in the snowmobile

Example QuestionExample Question Suppose an airplane drops Suppose an airplane drops

a “pleasant” package while a “pleasant” package while it is moving with a constant it is moving with a constant horizontal speed at an horizontal speed at an elevated height. Assuming elevated height. Assuming that air resistance is that air resistance is negligible, where will the negligible, where will the relief package land relative relief package land relative to the plane?to the plane?

a. below the plane and a. below the plane and behind it. behind it.

b. directly below the planeb. directly below the plane c. below the plane and c. below the plane and

ahead of itahead of it

Example QuestionsExample Questions

You are driving along in an open car You are driving along in an open car and throw a ball straight up into the air. and throw a ball straight up into the air. Neglect air resistance. Neglect air resistance.

(a) Where does the ball land relative to (a) Where does the ball land relative to the car?the car?

Answer:Answer: In the car. In the car.

(b) While the ball is still in the air you (b) While the ball is still in the air you step on the accelerator. Where does step on the accelerator. Where does the ball land relative to the car? the ball land relative to the car?

Answer:Answer: Behind the car. Behind the car.

(c) What if you stepped on the brake (c) What if you stepped on the brake instead?instead?

Answer:Answer: In front of the car. In front of the car.

Example QuestionsExample QuestionsYou drop a ball from the window of a You drop a ball from the window of a

school bus moving a 10 miles/hour. school bus moving a 10 miles/hour. Neglect air resistance.Neglect air resistance.

(a) Where does the ball land relative to (a) Where does the ball land relative to your hand?your hand?

Answer:Answer: Directly below your hand. Directly below your hand.

(b) What is the shape of the path made (b) What is the shape of the path made by the ball seen by someone outside by the ball seen by someone outside the bus?the bus?

Answer:Answer: A parabola. A parabola.

SummarizerSummarizer

What is a projectile?What is a projectile?What is the acceleration of a horizontally What is the acceleration of a horizontally

projected object in both the vertical and projected object in both the vertical and horizontal directions?horizontal directions?

Why will a projectile fired Why will a projectile fired horizontallyhorizontally hit hit the ground at the the ground at the same timesame time as an object as an object dropped from rest if they are released at dropped from rest if they are released at the same height?the same height?

Kinematic Equations

advv

atvv

tvv

d

attvd

if

if

fi

i

2

2

2

1

22

2

Ymax = maximum vertical displacement

Vy = final velocity at a given time in y-direction

Vyi = initial velocity in y-direction

Vx = final velocity in x direction

Vxi = initial velocity in x-direction

dx = total horizontal displacement

g = acceleration due to gravity

t = time xix

xx

yiy

yiy

yi

vv

tvd

gyvv

gtvv

gttvy

max22

2max

2

2

1

Projectile Motion Equations

Problem SolvingProblem SolvingFollow these steps to solve problems:Follow these steps to solve problems:

ReadRead Problem ProblemMake Make DiagramDiagramIdentify Identify KnownsKnownsIdentify Identify UnknownsUnknownsChoose Choose FormulaFormulaSolveSolve (and Check) (and Check)

Acronym Acronym R.D. KUFSR.D. KUFS (Mr. Hairston’s Rap Alias) (Mr. Hairston’s Rap Alias)

Horizontal ProjectionHorizontal Projection Once the cannon ball leaves the cliff, it Once the cannon ball leaves the cliff, it

experiences a downward acceleration experiences a downward acceleration equal to gravity. equal to gravity.

Thus the vertical velocity (Vy) is Thus the vertical velocity (Vy) is continually increasing.continually increasing.

The horizontal velocity (Vx) remains The horizontal velocity (Vx) remains constant and is equal to Vxo. constant and is equal to Vxo.

The two vectors Vx and Vy are added The two vectors Vx and Vy are added together to get the velocity at together to get the velocity at instantaneous points on the path. instantaneous points on the path.

When an object is shot horizontally When an object is shot horizontally from the from the same heightsame height, but with different , but with different force, it will always take the force, it will always take the same same amount of time to landamount of time to land. The bigger the . The bigger the initial force, the farther the object will initial force, the farther the object will travel, but they will all land at the same travel, but they will all land at the same time. time.

I DOI DO• A cannon shoots a cannon ball horizontally from a 24m high A cannon shoots a cannon ball horizontally from a 24m high

cliff, which lands 100m from the base of the cliff.cliff, which lands 100m from the base of the cliff.

a. With what velocity was the projectile fired?a. With what velocity was the projectile fired?

b. What is the projectiles velocity as it strikes the ground? b. What is the projectiles velocity as it strikes the ground?

WE DOWE DO A golf ball is projected with a A golf ball is projected with a

horizontal velocity of 30 m/s horizontal velocity of 30 m/s and takes 4.0 seconds to and takes 4.0 seconds to reach the ground. reach the ground.

a) What is the height from a) What is the height from which the golf ball was which the golf ball was projected? projected?

b) What is the resultant b) What is the resultant velocity just before the object velocity just before the object strikes the ground. strikes the ground.

c) How far did the ball go? c) How far did the ball go?

YOU DOYOU DOHarry and Angela look from Harry and Angela look from

their balcony to a swimming their balcony to a swimming pool below that is 15m from pool below that is 15m from the bottom of their building. the bottom of their building. They estimate the balcony They estimate the balcony is 45m high and wonder is 45m high and wonder how fast they would have to how fast they would have to jump horizontally to jump horizontally to succeed in reaching the succeed in reaching the pool. What do you think?pool. What do you think?