Notes: Notes: Projectile MotionProjectile Motion

Projectiles Projectiles are . . .are . . .•Objects thrown or launched into Objects thrown or launched into

the airthe air•While in the air, While in the air, gravitygravity is the is the

only force acting on them only force acting on them

Examples: Examples: FootballsFootballsAngry BirdsAngry BirdsKids who ride bikes off cliffs

Projectiles have 2 components Projectiles have 2 components to their motion . . .to their motion . . .

•Vertical Vertical acceleration acceleration due to gravity due to gravity

•Constant Constant Horizontal Horizontal Speed (0 Speed (0 acceleration)acceleration)

• This horizontal velocity also has no This horizontal velocity also has no acceleration – it is constant speedacceleration – it is constant speed

θ

V

Range = horizontal distance traveled

How do we deal with them?How do we deal with them?• Set up a double T-chartsSet up a double T-charts

X Yvf

v0

a

t

d

What will the acceleration What will the acceleration be?be?

X Yvf

v0

a

t

d

-9.8m/s20 m/s2

Same v

0 & vf

same same

How will the times compare?How will the times compare?

When launched at an angleWhen launched at an angle• Look at it like a right triangle,Look at it like a right triangle,

with the initial velocity as the with the initial velocity as the hypotenuse.hypotenuse.

• Find the x and y components of the Find the x and y components of the vv00

θVx

Vy

0

V0

X Yvf

v0

a

t

d

-9.8m/s20 m/s2

When asked for maximum When asked for maximum heightheight• Only half of the time has passedOnly half of the time has passed

θ

V

Max H

eig

ht

½ time in the air = max

height

Other important Other important information:information:• For all of our problems we ignore friction For all of our problems we ignore friction

– which can affect path shape and – which can affect path shape and motion motion

• Projectile motion is a parabola shapeProjectile motion is a parabola shape

• Trajectories of 45Trajectories of 45° will have the ° will have the greatest height and rangegreatest height and range

• At max. height vertical v = 0m/s At max. height vertical v = 0m/s

• Initial velocity and final velocity are the Initial velocity and final velocity are the same, but in different directionssame, but in different directions

Projectiles launched Projectiles launched horizontallyhorizontally

Cliff

• This is just a This is just a drop with drop with forward motion forward motion added.added.

Vertical vVertical vii = 0m/s = 0m/sYvf

vi 0

a -9.8

t

y

xvf

vi

a 0

t

x

Example 1:Example 1:

• A bike is ridden off of a 25 m cliff at A bike is ridden off of a 25 m cliff at 15 m/s. Solve for everything!!!15 m/s. Solve for everything!!!

Example 2:Example 2:

• A boy shoots a slingshot horizontally A boy shoots a slingshot horizontally off a cliff at 20 m/s. It lands 100 m off a cliff at 20 m/s. It lands 100 m from the base of the cliff. Solve for from the base of the cliff. Solve for everything!!!everything!!!