Tueday, Mar. 11 Do Now

What is free fall?

Summary of Chapter 2 – Free Fall-Free fall is the motion of an object being acted on only by gravity.-Acceleration due to gravity is approximately 10 m/s2.-An object dropped from rest will accelerate from a velocity of zero to 10 m/s after dropping 1 meter.

acceleration due to gravity = g= 10 m/s2

-If an object is thrown upwards, it will decelerate (have negative acceleration or slow down) at a rate of 10 m/s2.

-The instantaneous velocity of an object falling from rest after a time interval of t is:

v = gt-The distance traveled by an object in free fall is given by:

d = ½ gt2

-The distance traveled and velocity of an object being accelerated by any force is given by:

d = ½ a t2 v = at

Introduction

Projectile Motion:

Motion through the air without a propulsion Examples:

Motion of Objects Projected Horizontally

x

y

x

y

x

y

x

y •Motion is accelerated•Acceleration is constant, and downward• a = g = -9.81m/s2 •The horizontal component of velocity is constant•The horizontal and vertical motions are independent of each other, but they have a common time

g = -9.81m/s2

ANALYSIS OF MOTION

ASSUMPTIONS:

• x-direction (horizontal): uniform motion

• y-direction (vertical): accelerated motion

• no air resistance

QUESTIONS:• What is the trajectory (path of motion)?• What is the total time of the motion?• What is the horizontal range?• What is the final velocity?

Wednesday, Mar. 12 Do Now

Which object hits the ground first:-an object dropped from rest, or-an object that is moving with a horizontal velocity before being dropped? Explain why.

x

y

0

Frame of Reference:

h

v0

Equations of motion:

X Uniform Motion

YAccelerated

Motion

ACCL. ax = 0 ay = g = -9.81 m/s2

VELC. vx = v0 vy = g t

DSPL. x = v0 t y = h + ½ g t2

g

Trajectory

x = v0 t

y = h + ½ g t2

y

x

hParabola, open down

v01v02 > v01

Total Time, Δt

y

x

hti =0

tf =Δt

Total time of motion depends only on the initial height, h

Δt = tf - ti

Horizontal Range, Δx

y

x

h

Horizontal range depends on the initial height, h, and the initial velocity, v0

Δx

x = v0 t

Thursday, Mar. 13 Do Now

Which object hits the ground first:-an object dropped from rest, or-an object that is moving with a horizontal velocity before being dropped? Explain why.

x

y

0

Frame of Reference:

h

v0

Equations of motion:

X Uniform Motion

YAccelerated

Motion

ACCL. ax = 0 ay = g = -9.81 m/s2

VELC. vx = v0 vy = g t

DSPL. x = v0 t y = h + ½ g t2

g

Trajectory

x = v0 t

y = h + ½ g t2

y

x

hParabola, open down

v01v02 > v01

Total Time, Δt

y

x

hti =0

tf =Δt

Total time of motion depends only on the initial height, h

Δt = tf - ti

Horizontal Range, Δx

y

x

h

Horizontal range depends on the initial height, h, and the initial velocity, v0

Δx

x = v0 t

Wed. March 19 Do Now:In the Bull’s Eye lab, what is the formula you used to calculate:

speed of your marble:

the time is takes for the marble to fall to the ground:

So far we have looked at motion of objects in free fall and motion

as an object is projected horizontally.

Now we will look at objects projected at an angle.

Examples:Free Fall Object projected horizontally

Examples of Projectiles at an Angle

x

y

• Motion is accelerated• Acceleration is

constant, & downward• a = g = -9.81m/s2 • The horizontal (x)

component of velocity is constant.

a = g =

- 9.81m/s2

The horizontal & vertical motions are independent of each other, but they have a common time.

ANALYSIS OF MOTION:

ASSUMPTIONS

• x-direction (horizontal): constant velocity

• y-direction (vertical): accelerated motion

• no air resistance

QUESTIONS• What is the path of motion?• What is the total time of the motion?• What is the horizontal range?• What is the maximum height?• What is the final velocity?

Path Of Motion – parabola, open down

x

Δx

y

0

Assumes no air resistance

Δx is the horizontal range

Trajectory and horizontal range

0

5

10

15

20

25

30

35

0 20 40 60 80

15 deg

30 deg

45 deg

60 deg

75 deg

vi = 25 m/s

•CONCLUSIONS:•Horizontal range is greatest for the throw angle of 450

•Horizontal range is the same for 30o & 60o launch angles. gree

Velocity

•Final speed = initial speed (conservation of energy)

•Impact angle = - launch angle (symmetry of parabola)

PROJECTILE MOTION - SUMMARY Projectile motion is motion with a constant

horizontal velocity combined with a constant vertical acceleration

The projectile moves along a parabola

Class Work/Homework

P. 40-42 #7-10, 12-14, 34, 42-44, 46

Thurs. March 20 Do Now: Describe the differences between free fall, motion of an

object projected horizontally, and motion of an object projected at an angle.

Two objects projected from a cliff at the same time. One object is dropped straight down from the cliff. The other object is pushed off the cliff horizontally with a velocity of 10 m/s. Which one will hit the ground first?

Shooting rubber balls out of fixture demo Review of projectiles Quiz