projectile motion i 11/7/14. throwing a ball in the air on the way up: at the top of the throw: on...

Projectile Motion IProjectile Motion I

11/7/1411/7/14

Throwing a ball in the airThrowing a ball in the air

• On the way up:

• At the top of the throw:

• On the way down:

• velocity decreases • acceleration stays the

same.• velocity zero • acceleration stays the

same.• velocity increases • acceleration stays the

same.

Throwing a ball in the airThrowing a ball in the air

• The velocity changes.

• The acceleration is constant, it stays the same 9.81 m/s/s, downward throughout the flight.

ProjectilesProjectiles

• Projectiles: are objects where gravity and air resistance are the only forces acting

• Projectiles travel with a parabolic trajectory (path)

ProjectilesProjectiles

• A projectile’s horizontal component is independent of the vertical component

• The force of gravity does not affect the horizontal component of motion

• (i.e.) What is happening left and right does not effect what is happening up and down

Air ResistanceAir Resistance

• Air Resistance: A force of friction that acts on an object moving through the air

• For projectile motion we will often neglect or assume that air resistance is extremely small

Projectile TermsProjectile Terms

• Range: The distance a projectile travels horizontally from the initial position.

• Max Height: The greatest distance a projectile travels vertically

• Hang Time: The total amount of time a projectile is in the air

ComponentsComponents

• Component: the projection of a vector quantity along a perpendicular axis

ComponentsComponents

Horizontal

• Right = +x

• Left = -x

Vertical

• Up = +y

• Down = -y

Projectile QuantitiesProjectile Quantities

• Displacement (m)

x = horizontal displacement

y = vertical displacement

• Velocity (m/s)

vx = horizontal velocity

vy = vertical velocity

Projectile QuantitiesProjectile Quantities• Acceleration

ax = 0 m/s2 (no horizontal acceleration)

ay = -9.80 m/s2 or “g”

• Time (s)

t = time

- Does not depend on direction (scalar)

- It is the same for horizontal and vertical components

Projectiles and TimeProjectiles and Time

• (i.e.) A projectile has the same time for how long it goes up and/or down AND left or right

Mythbusters Mythbusters

• Dropped vs. Fired Bullet

Projectile Motion IIProjectile Motion II

11/10/1411/10/14

Quantity HorizontalComponent

Vertical Component

DisplacementYes,

same distanceeach second

Yes, different

distances each second.

VelocityYes,

ConstantYes, changing by -9.81 m/s each second.

Acceleration NoYes, constant

9.81 m/s/s, downward

“g”

Projectile Example

•What happens to a projectile’s horizontal and vertical displacement, velocity and acceleration?

•Example: An object with a initial horizontal velocity of 20 m/s to the right and vertical velocity of 0 m/s.

Displacement

Time HorizontalDisplacement

VerticalDisplacement

0 s 0 m, right 0 m

1 s 20 m, right 5 m, down





Velocity

Time HorizontalVelocity

VerticalVelocity

0 s 20 m/s, right 0 m/s

1 s 20 m/s, right 10 m/s, down





Acceleration

Time HorizontalAcceleration

VerticalAcceleration

0 s 0 m/s/s 10 m/s/s, down






A Falling Object

A falling object

Projectile (Horizonal)Projectile (Horizonal)

Projectile (Launched)Projectile (Launched)

Projectile GraphProjectile Graph

• Graph Due Wed. 11/12/14

Projectile Motion IIIProjectile Motion III

11/12/1411/12/14

Projectile EquationsProjectile Equations

Remember RIDGES (10/20)Remember RIDGES (10/20)

• R – Read the problem carefully!• I – Identify what you are looking for and the

Information that is given. (1 & 2 in T-Chart)

• D – Draw a picture of the problem.• G – Generate a plan (T-Chart)• E – Evaluate the Equation(s) that can help

solve the problem (3 T-Chart)• S – Solve the problem and answer with the

appropriate units (4 & 5 in T-Chart)

Projectile ProblemsProjectile Problems

1. Draw a sketch of the problem to determine horizontal and vertical components

2. Use a T-Chart to organize the problem

3. Time (often needed to be solved for 1st) is a scalar, it is the same for the horizontal and vertical components

Projectile ProblemsProjectile Problems

• 2 Types of problems:

– “Horizontally” from a height

– “Launched” from the ground

Projectile “Horizontal” ExampleProjectile “Horizontal” Example

• A tennis ball rolls off a lab bench that is 1.1 m high with a horizontal velocity of 3.7 m/s.

• a) How long will it be in the air for?• b) How far from the table does it land?• c) What is the ball’s vertical velocity as

it hit the ground?• d) What is the ball’s resultant velocity

as it hits the ground?

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