3.3 Projectile Motion3.3 Projectile Motion

From Ch 3 – Two dimensional From Ch 3 – Two dimensional Motion and VectorsMotion and Vectors

Half ProjectileHalf Projectile

Vx tVx t

yy

xx

EquationsEquations

y = ½ g ty = ½ g t22 or or t = sq rt 2 t = sq rt 2 y / gy / g

gg = -9.81 m/s= -9.81 m/s22

x = Vx t (Vx is constant)x = Vx t (Vx is constant)

Example of Half ProjectileExample of Half Projectile

People in movies often jump from buildings People in movies often jump from buildings into pools. If a person jumps horizontally into pools. If a person jumps horizontally form the 10form the 10thth floor (30.0 m) to a pool that is floor (30.0 m) to a pool that is 5.0 m away from the building with what 5.0 m away from the building with what initial speed must the person jump?initial speed must the person jump?

y = 30.0 my = 30.0 mx = 5.0 mx = 5.0 mVx = ?Vx = ?

Find t and then VxFind t and then Vx

t = sq rt 2 t = sq rt 2 y / ay / agg

t = sq rt 2 (-30.0m) / -9.81 m/st = sq rt 2 (-30.0m) / -9.81 m/s22

t = sq rt 6.1 s t = 2.4 st = sq rt 6.1 s t = 2.4 s

x = Vx t or Vx = x = Vx t or Vx = x / tx / t

Vx = 5.0 m / 2.4 s = 2.1 m / sVx = 5.0 m / 2.4 s = 2.1 m / s

Practice Activity: Homework WS and pg 99 1-3Practice Activity: Homework WS and pg 99 1-3

Full ProjectilesFull Projectiles

Anatomy of a Full ProjectileAnatomy of a Full Projectile

Vi Vi 22 = Vx = Vx 22 + Vy + Vy2 2 Vx = Vi cos Vx = Vi cos Vy = Vi sin Vy = Vi sin

Vi Vy Vi Vy

VxVx

More AnatomyMore Anatomy

x = Vx t x = Vx t y = (vi sin y = (vi sin ) t + ½ at) t + ½ at22

tttottot = 2 ( Vy / g) = 2 ( Vy / g)

t t yy t t

XX

Equations for a Full ProjectileEquations for a Full Projectile

Vi Vi 22 = Vx = Vx 22 + Vy + Vy22

Vx = Vi cos Vx = Vi cos = constant = constant x = (Vi cos x = (Vi cos ) t or ) t or

X X tottot = Vx ( t = Vx ( t tottot))

t t tottot = 2 ( Vy / g) = 2 ( Vy / g)

A Projectile is fired at an angle of 53A Projectile is fired at an angle of 53oo with the horizontal. The with the horizontal. The speed to the projectile is 200. m /s. A. Calculate the time the speed to the projectile is 200. m /s. A. Calculate the time the shell in air and the horizontal distance it travels.shell in air and the horizontal distance it travels. B. Calculate the maximum height reached.B. Calculate the maximum height reached.

Sin 53Sin 53oo = Vy / 200 Vy = 159.7 m/s = Vy / 200 Vy = 159.7 m/s

tttottot= 2 X 159.7 / 9.81 = 32.56 = 32.6 s= 2 X 159.7 / 9.81 = 32.56 = 32.6 s

Cos 53Cos 53oo = Vx / 200 = Vx / 200 Vx = 120.36 = 120. m/sVx = 120.36 = 120. m/s

xxtottot = 120 ( 32.6) = 3912 m = 120 ( 32.6) = 3912 m

y = (159.7 m/s) 16s + ½ (-9.81 m/sy = (159.7 m/s) 16s + ½ (-9.81 m/s22) (16 s)) (16 s)22 = 1300 m = 1300 m

Big BerthaBig Bertha

Big Bertha WW1Big Bertha WW1

RelativityRelativity

Our perspective is that we are stationary and Our perspective is that we are stationary and everything else is moving.everything else is moving.

When you are driving down the road and someone pulls up When you are driving down the road and someone pulls up next to you they look like they are not moving. You are next to you they look like they are not moving. You are going at the same velocity ( same speed and direction)going at the same velocity ( same speed and direction)

RelativityRelativity

When a car is coming directly at you. You attribute When a car is coming directly at you. You attribute your speed to them. The red car is traveling at 50 your speed to them. The red car is traveling at 50 mph and the blue car is traveling at 60 mph. mph and the blue car is traveling at 60 mph.

It appears as if the other car is traveling at 110 mph toward you.It appears as if the other car is traveling at 110 mph toward you.

RelativityRelativityYou are riding in a car and look and see a person You are riding in a car and look and see a person

standing along side the road.standing along side the road.

The guy appears The guy appears

to be moving but in to be moving but in

the opposite the opposite

direction you are direction you are

traveling.traveling.

What would you see?What would you see?

Wrap UpWrap Up

Review sheet is dueReview sheet is due

Marble ActivityMarble Activity

TestTest