Free Fall

Motion Notes Day 4

Galileo Galilei

• 1564 - 1642• Galileo formulated the

laws that govern the motion of objects in free fall

Free Fall

• All objects moving under the influence of gravity only are said to be in free fall– Free fall does not depend on the object’s

original motion• All objects falling near the earth’s surface

fall with a constant acceleration• The acceleration is called the acceleration

due to gravity, and indicated by g

Acceleration due to Gravity

• Symbolized by g• g = -9.8 m/s2

• g is always directed downward– toward the center of the earth

• Ignoring air resistance and assuming g doesn’t vary with altitude over short vertical distances, free fall is constantly accelerated motion

Free Fall – an object dropped

• Initial velocity is zero• Let up be positive• Use the kinematic equations• Acceleration is g = -9.8 m/s2

vi= 0

a = g

Free Fall – an object thrown downward

• a = g = -9.8 m/s2

• Initial velocity ≠ 0– With upward being

positive, initial velocity will be negative

Vi= (-)

a = g

Free Fall – an object thrown upward

• a = g = -9.8 m/s2

• Initial velocity ≠ 0– With upward being

positive, initial velocity will be positive

• final velocity = 0

Vi= (+)

a = g

Free Fall - Example

2

0

??

??

9.8

18sec

i

f

mV

sV

d

ma

st

1 2V t ati 2

1 20 (-9.8)(18)2

1587.6 m

therefore height of

building is 1587.6 m

d

d

d

If a rock is dropped from a building, and it takes 18 seconds to reach the ground, how tall is the building?

PracticeA baseball is thrown up vertically with a velocity of 12

m/s. a. What is the maximum height the baseball reaches? b. How long does it take to reach max height?c. What is the velocity when it hits the ground?

PracticeA baseball is thrown up vertically with a velocity of

12 m/s. a. What is the maximum height the baseball reaches?

2

12

0

??

9.8

??

i

f

mV

sV

d

ma

st

2 2

2 2

2 2

2

( ) / 2

(0 12 ) / 2( 9.8)

144 / 19.6

d= 7.3 m

f i

f i

V V ad

d V V a

d

d

PracticeA baseball is thrown up vertically with a velocity of

12 m/s. a. d= 7.3 m (We can use this now!!)b. How long does it take to reach max height?

2

12

0

7.3

9.8

??

f

mVi

sV

d m

ma

st

( ) /

(0 12 ) /( 9.8)

12 / 9.8

t = 1.22 s

f i

f i

V V at

t V V a

t

t

PracticeA baseball is thrown up vertically with a velocity of 12

m/s. a. d= -7.3 m (negative because falling!!)b. t= 1.22s (We can use this now!!)c. What is the velocity when it hits the ground? (Now we

assume falling with Vi = 0)

2

0

??

7.3

9.8

1.22

i

f

V

V

d m

ma

st s

0 ( 9.8)(1.22 )

12 /

same magnitude, but

opposite direction as

when thrown up

f i

f

f

i

V V at

V s

V m s

V

Homework

• Complete 1-16 on 1D Kinematics Worksheet• Answers will be posted on Website!!!• Tomorrow and Friday we will review graphing• Quiz Friday• Motion Test Thursday, Sept 12!!!

Position-time graphs show how the position of an object changes over time.

t

d

x

y line of slope

So, the slope of a d/t graph tells us the VELOCITY of the object.

Velocity-time graphs show how the velocity of an object changes over time.

t

v

x

y line of slope

So, the slope of a d/t graph tells us the ACCELERATION of the object.

The slope is constantly changing, so that means the velocity is changing. Changing velocity is called ACCELERRATION.

The area under the graph represents displacement (Δd).