This document discusses projectile motion and common misconceptions about how objects move when thrown off cliffs or launched horizontally. It describes a study where most students of all ages incorrectly believed that a horizontally launched object would pause in mid-air before falling straight down. Simulations and experiments show that horizontal and vertical motion are independent, so a rolling ball would follow path C and continue moving forward as it falls due to the independent effects of its initial horizontal velocity and gravity's downward acceleration. The key lesson is that horizontal motion does not affect an object's time to fall or its downward motion.

1. Projectile
Motion
…it’s as easy as rolling off a
cliff…

2. Prediction
› Before
you
par+cipated
in
the
PhET
simula+on,
you
made
a
predic+on
and
explained
your
reasoning
to
me
via
email.

3. A Little History…
A
few
years
ago,
researchers
went
to
elementary,
middle,
and
high
schools
as
well
as
universities
and
showed
students
this
image
and
asked
them,
Ignoring
air
resistance,
which
of
the
following
correctly
shows
what
an
object
would
do
if
it
rolled
off
a
cliff?”

4. The Results
› The
breakdown
of
answers
they
got
was
almost
exactly
the
same
at
all
ages.
› About
60%
said
“A”
was
correct.
The
object
will
stop
in
midair,
and
then
start
to
fall
straight
down.
Because
some
people
referred
to
the
coyote
in
cartoons,
the
researchers
called
it
the
Wile
E.
Coyote
Effect.
› About
25%
said
“B”
was
correct.
The
object
will
move
forward
at
first,
but
will
eventually
just
fall
straight
down.
› About
15%
answered
“C”.
The
object
will
con+nue
to
move
forwards
the
en+re
+me
it
is
falling.

5. So What’s the Correct Answer?
› I’m
not
going
to
tell
you.
We’ll
revisit
the
ques+on
at
the
end
of
these
notes.
J

6. Observations
from
the
Simulation
§ As
we
saw
with
the
simula+on,
the
projec+le
that
fell
straight
down
and
the
one
that
was
shot
from
a
cannon
horizontally
-­‐
hit
the
ground
in
the
same
amount
of
+me.
§ So
what
effect
did
horizontal
velocity
have
on
the
+me
it
took
(the
downward
mo+on
of)
the
projec+le
to
hit
the
ground?
§ None!
§ The
best
conclusion
we
can
make
from
this
is
that
the
horizontal
mo+on
of
a
projec+le
does
not
affect
downward
mo+on
of
the
projec+le.

7. Observations
from
the
lab
› Intui+on
will
tell
you
that
the
horizontally
launched
object
will
“hang”
in
the
air.
› But…
› YOUR
INTUITION
(at
least
in
this
case)
IS
WRONG!
› Here’s
a
video
› Here’s
another
video

8. Horizontal and Vertical Motion
› The
most
important
thing
you
can
remember
about
projec+le
mo+on
is
this:
› Horizontal
and
Ver+cal
mo+on
are
completely,
100%
INDEPENDENT
of
each
other
–
even
when
they
are
happening
at
the
same
+me.
› Your
lab
ques+on
was,
“How
does
ini+al
velocity
affect
the
amount
of
+me
it
takes
a
horizontally-­‐
launched
object
to
reach
the
ground?”

9. Does Horizontal Affect Vertical?
› The
short
answer
to
the
lab
ques+on
is:
› It
Doesn’t!
The
horizontal
mo+on
of
the
projec+le
is
unaffected
by
the
downward
(ver+cal)
force
of
gravity.
› What
does
affect
how
long
it
takes
an
object
to
hit
the
ground
(ignoring
air
resistance)?
› One
thing
and
one
thing
only…
› The
height
it
is
launched
from!

10. Looking at velocity vectors
› On
the
next
slide,
we’re
going
to
look
at
the
paths
two
projec+les
follow.
One
projec+le
is
shot
out
of
a
cannon,
the
other
is
dropped
at
exactly
the
same
moment.
› yes,
just
like
the
lab
J
› When
going
through
the
slide,
remember:
› velocity
is
a
vector
(has
magnitude
&
direc+on)
› gravity
is
a
constant
force
› constant
forces
cause
accelera+on

11. While
clicking
through
this
slide,
keep
in
mind
that
the
law
of
iner+a
tells
us
that
objects
in
mo+on
stay
in
mo+on
at
a
constant
speed
and
in
a
straight
line.
Since
horizontal
mo+on
is
independent
of
ver+cal
mo+on,
the
horizontal
vector
never
changes!
two
cannon
balls
–
one
is
given
a
horizontal
force,
the
other
is
just
dropped
gravity
acts
downward
on
both
horizontal
mo+on
con+nues
gravity
is
a
constant
force
that
accelerates
all
falling
objects
(ignoring
air
resistance)
gravity
acts
on
all
objects
equally

12. Back to the cliff…
So…which
path
will
the
red
ball
travel?
It
will
follow
path
C
–
because
its
horizontal
mo+on
will
con+nue
at
the
same
speed
and
direc+on
(law
of
iner+a)
while
gravity
exerts
a
downward
force
at
the
same
+me!

13. Reflection
› As
we
saw
with
the
ball
and
the
cliff
ques+on,
many
people
–
even
highly
educated
people
–
have
misconcep+ons
about
falling
objects
versus
objects
with
a
high
horizontal
velocity.
› Ask
five
of
your
friends
or
family
members
which
bullet
will
stay
in
the
air
longer:
one
shot
from
a
pistol
or
one
dropped
from
pistol
height.
(Obviously,
don’t
ask
students
in
this
class
or
physics
majors
J)

14. Reflection
› On
the
discussion
board
page,
join
the
discussion
about
why
you
think
most
people
have
the
misconcep+on
that
a
bullet
fired
from
a
gun
will
“hang”
in
the
air.
What
is
it
about
a
bullet
from
a
gun
(or
an
arrow
from
a
bow
and
arrow,
or
a
cannon
ball
out
of
a
cannon,
etc.)
that
makes
it
so
hard
to
believe
that
gravity
acts
on
it
exactly
the
same
way
gravity
acts
on
an
object
with
no
horizontal
velocity
(ie,
one
that
is
dropped)?
› Make
one
original
post
and
respond
to
at
least
two
other
student’s
posts.