• Self evaluation

• Tickets

• Class officers

How are the vertical and horizontal components analyzed in 2 dimensional projectile motion?

http://www.youtube.com/watch?v=0epHS1D-Swohttp://www.youtube.com/watch?v=D9wQVIEdKh8

-An object upon which the only force acting is gravity which causes the object to curve downward along a parabolic path known as a trajectory

Projectile

• HORIZONTAL LAUNCH– Vyi= 0 m/s not moving

vertically– yi> 0 m launched above

ground– Vxi> 0 m/s moving

horizontally

https://www.youtube.com/watch?v=EREQEy2tOxo

• ANGLE LAUNCH– Vi > 0 m/s

• find x and y components to get Vxi and Vyi

– Highest point (ymax)• Vy= 0 m/s• Half of time

http://www.youtube.com/watch?v=3wAjpMP5eyo

2

t

2 types of projectile:

2 types of projectile:Horizontal Component Vertical Component

Forces present/not present

Acceleration present/not present

Velocity constant/changing CONSTANT

NOYes – downward g = -9.80 m/s2

NOYES - GRAVITY

CHANGING

Projectile Characteristics

1. Supposing a snowmobile is equipped with a flare launcher that is capable of launching a sphere vertically (relative to the snowmobile). 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 snowmobileb. behind the snowmobilec. in the snowmobile

2. Consider these diagrams in answering the following questions. Which diagram (if any) might represent ...a. ... the initial horizontal velocity?b. ... the initial vertical velocity?c. ... the horizontal acceleration?d. ... the vertical acceleration?e. ... the net force?

Check Point

HORIZONTAL LAUNCH

constant xi vv

tvx x

2)(2

1tgy

Things to note:*g= 9.80 m/s2

*viy = 0 m/s

ANGLE LAUNCH

constant

)(cosix vv

tvx i )(cos

tgvv ify )(sin,

ygvv ify 2)(sin 222,

2)(2

1)(sin tgtvy i

Example 1 of horizontal projectile

• A movie director is shooting a scene that involves dropping a stunt dummy out of an airplane and into a swimming pool. The plane is 10.0 m above the ground, traveling at a velocity of 22.5 m/s in the positive x direction. The director wants to know where in the plane’s path the dummy should be dropped so that it will land in the pool. What is the dummy’s horizontal displacement?

Example 2 of Horizontal Projectile

G: Initial velocity is zero

Because it is in free fall, a becomes g

U:

sms

m

t

xv /56.5

09.8

45

Horizontal (x) Vertical (y)

x = 45.0 m viy = 0 m/s

g = -9.80 m/s2

vix = ? y = -321 m

Velocity initial in x direction

E:

S:

S: Vx = 5.56 m/s

First solve for t with given info

Usually if a vertical equation is used to solve for time, then a horizontal equation can be used to find the unknown quantity or vice versa

Example 3 of Horizontal Projectile

Florence Griffith-Joyner of the United States set the women’s world record for the 200 m run by running with an average speed of 9.37 m/s. Suppose Griffith-Joyner wants to jump over a river. She runs horizontally from the river’s higher bank at 9.37 m/s and lands on the edge of the opposite bank. If the difference in height between the two banks is 2.00 m, how wide is the river?

G: Initial velocity is zero

Because it is in free fall, a becomes g

U:

Horizontal (x) Vertical (y)

x = ? viy = 0 m/s

g = -9.80 m/s2

vix = 9.37 m/s y = 2.00 m

X – width of river

E:

S:

S: X = 5.99 m

First solve for t with given info

Usually if a vertical equation is used to solve for time, then a horizontal equation can be used to find the unknown quantity or vice versa

Example 1 of Projectiles at an Angle

A baseball is thrown at an angle of 25°relative to the ground at a speed of 23.0 m/s. If the ball was caught 42.0 m from the thrower, how long was it in the air?

How high was the tallest spot in the ball’s path?

A soccer player kicks a soccer ball towards the goal. If he kicks it with a velocity of 24 m/s at an angle of 31

degrees, how far will the ball travel?

Example 2 of Projectiles at an Angle

G:

U:

G = 9.80 m/s2

Vyf = 0 m/sVi = 24 m/s = 31°

Distance in horizontal (x) direction

E:

S:

S: X = 52 m

2)(2

1)(sin tgtvy i

2)(2

1)(sin0 tgtvi

a. the ball’s hang time

b. the ball’s maximum height

c. the horizontal distance the ball travels before hitting the ground

A player kicks a football from ground level with an initial velocity of 27.0 m/s, 30.0° above the horizontal, Find each of the following. Assume that forces from the air on the ball are negligible.

EXAMPLE 3 OF PROJECTILES AT AN ANGLE

G:

U:

G = 9.80 m/s2

Vyf = 0 m/sVi = 27.0 m/s = 30.0°

Time in air (t)Max height (y)Distance in horizontal direction (x)

E:

S:

S:

a.

T = 2.76 s

t= 1.377*2 = 2.755

E:

b.

S:

S:

2)(2

1)(sin tgtvy i

2)38.1)(80.9(2

1)38.1)(0.30)(sin0.27( y

Maximum hieght occurs at half the hang time. T= 2.76/2 = 1.38 s. Thus,

Y = 9.30 m

G = 9.80 m/s2

Vyf = 0 m/sVi = 27.0 m/s = 30.0°

G:

E:

S:

S:

Distance in x direction