we're going to take it
quite easy
i'll also have to take it a little easy
put my voice
maybe
petering out the final careful
we're going to apply today
what we have worked so there's nothing
new
this application
that's important things that
you can let it sink in
we have here
the trajectory of a global or tennis
balls
twenty six one hundred
we showed up at an angle all fine
the horizontal components
in the excel actions be zero co-signed
all fine
and a political component is the zero
sign off on
it which is the highest point at the
peak
and at the returns to the ground f point
s
this is the
increasing light election and is it
increasing extent reaction
we're going to use
very heavily
the equations
that you see here
that are so familiar with us
these are the one that meant you know he
creations in excel recommenders and
where there's no acceleration
and will not mention only christians in
the whitewater committee is coverage
in order to use these equations we need
all these constant x zero
the zero x and easier or what
we've seen those last time
i'd choose for example
are choosing zero arbitrarily also four
white zero
the velocity accel action will never
changed is the zero x
will always remain d zero call sign off
on
the velocity in the white arm action
however
in the beginning at people zero
is the zero sign off on
and that one will change because that is
here
instinct that's why
the velocity is going to change these
people do it
an acceleration in the white election
invaded increasing value off wife
is going to be negative nine point eight
in cycle always nine point eighty plus
attendant was kool g
plus nine point eight
this is uh...
minus
i know
want to ask first the question
that you may never have seen answers
what is the shape of these well
we can go to increase the number three
there
and we can write down integration number
three
that's why
as a function of time
equals the zero whitey
but it is to be zero
signed all clock
arms clean
minus
one haha
gts quit
that he creation and why i go to
equation number one
and i write down
at any moment in time
equals the zero x times g
so that it's been zero
co-sign all-star
dot com
now i eliminate g
and the best way to do that is to do
with here right forty px
x
divided by a
the hero
co-signed also
now i can draw ball sup indexes t
because we're not going to see x
which is why
we're going to eliminate t
so this time of year
i'm going to substitute india and in the
air
and so i'm going to get wider
equals
there's a view your role here
and is it easy rodeo
the cancels there is a sign off by the
year anna co-sign also there
that makes it depends in bhopal fuck
and then i have your
x
and i get minus
one-half of g
thank these script
excreted
defined by
the zero
co-signed wildfire
squid
and i look very carefully
why is it cold sometimes acts
minors under constant
thanks x
squeaked dot
these parabola second-order equation
index
and his brother and the parabola
has to be straight
till you see no by eliminating the time
that we have here
now i want to massages
quite a bit further today
i would like to know
uh... at launch time
you object here
goes to work
wholefoods highest points
comes through the whole thing the white
election comes to the highest point and
i wanna know how high that
is
well
the best way to do is to go to leak
region four
and to take a vacation for when are you
general
because that is the moment that the
velocity into wider action becomes zero
it must be at its highest point in
so in order to find for us
the position off
the highest point three
me first ask ourselves the question
for recreation
number
foreigner
when is the velocity in the white action
zero
and that then becomes
the zero y which is
the zero signed all fun
minus
g_t_
and i'll call step he at point pete
i'm going to be
the zero signed all pop
divided by
that's the time of the cakes for the
object
to reach the highest point
where is it that
what is the hottest points
above the ground
well now you have to go to recreation
number three
and you have to substitute this time in
the air
soul
that high at this point age
which is why at the time she offbeat
uh...
equals
the zero white sea
that is the zero
time to sign of all fine
but they have to multiply its
by this time
and so i get a note of the zero style
font
and i get a g here
minus
duty
michael no no
it's a great might haha the peace corps
minus one haha
g by this one squint
because the zero
signed all file
grant
divided by
divided by g script
but there's a g here you see seems
credible finkelstein squid
you don't want to meet
and you'll find them
that the highest points
that's right down here so that we don't
bloke that blackboards
the highest points
discarded equals
the zero
signed all fine
quit
divided by
that is the highest point let's give it
to them
because we may want to
in reasonable doubt that points
with highest point in the sky
gets higher wendy zero does high of
course
if i showed up
at a higher speeds of course it will get
high
tortoise completely intuitive
but the zero was upstairs
if i would increase the angle
form a small angle to larger and larger
than larger
is it a reasonable that it'll get higher
of course
no love for you
in your stomach but the highest possible
though you can get it by you bring your
make
often ninety degrees forgiven velocity
that's the highest it will go in the sky
so clearly this is also very pleasing
if you get the experiment on the moon
with the same initial speed it'll go
much higher so you also have been
conceded the
used on status
for that make sense
at what time
will be object b
at point asks
well have to wait to get into that
either go to this equation number three
and you ask a greater number three when
i use zero
will give you two answers
will say i'm zero here at this time
and i'm here at that time and ordered it
two times that you want and this is the
one you pick
that's perfectly fine
i think is a faster way to do with
and that's the following
this is a parabola source completely
symmetric about the protocol about p
so to climb up from old two p mostly the
same amount of time is to go down from p
two s
and so i claim at the time
point asp
must be
twice define reached a point pete
and therefore it's going to be two b
zero
a final fight
reporting
now
we want to walk again
wedded to the zeroed in to sign off of
have the right place
in dat if i i think reached its peak
i will be expected to take longer
before it leeches ants
if i give it a larger speak
it will come out forever
obviously
time will take longer
if i do it had a hard angle
it will also take care
and if i do it on the moon
which will also take a moment
so this makes sense
you please use
appraising in terms of their
the reiki zero and final cut
appealing creations
that malcolm's importance
point which i did
bring to you throughout his lecture
i want to know what elastase
the distance olis
i'm sure deduct and it hits the floor
again
what is that this means that it travels
well for that
i need to be creation
number one
because the zero x time to time
andy zero x
is set in
the zero co-signed all fine
you get the zero
kortunov out
thank the prime convicted students to p
zero sign all fine
so we get it to you
against final cut
and i get a g_p_s_
and i have another
d zero there
and sold the answer is
v zero scripts
find the sign of the day
double angle remembered too
court and also sign allspice assignments
who all fun
divided by t
and this is all that's
and wouldn't be dissolved
is reminds me
knots too
remove it
now
i sort of wonder and you should too
why is it that the highest point in the
sky
hasn t zero squid
and why is the part of sports
also wanted to also have the zero square
might be a way that you can reason that
why did not just a year or two b zero
square
well i'd like to argue about the highest
points
and i give you a good reason
for the
distance alas
dot org wiki equations
distinctly
for change
notebookreview creations
all right
double the speed
if i don't know the speed
it's quite reasonable that the find that
it takes
forty objects to reach the ground
real double
brats
well the time that implies has doubled
the horrors on vocalocity has
also doubles
and so did this and that it will travel
in horizontal direction
four times that
twice because the times
has doubled
and another factor of two
because the horizontal components
has also doubles
so that's why you see v zero square
there
completely pc
this tokyo immediately that
the if you want to throw a ball as far
as possible
people who played baseball know that you
should do it at forty five degrees
because if you saw in forty five degrees
it's angle
ninety degrees that as well
of course
in reality
a baseball player knows better they get
the fact of the bull
beginnings and read
expendable
and he creations
uh... arnold's elegance is only in case
we do you guys
respected
and i would like to
some of the results that we have here
we have worked out here
i'm going to shoot eighty
ballots and
metal bowl
i'm going to show you that various
angles
thirty degrees sixty degrees forty five
degrees
and i'm going to make a prediction
if i showed it up from there
report at the table
the measurements
is meaningless
without
knowing
the uncertainties
but that's the first thing we have to
deal with us
the first thing i wanna know is what is
the velocity
of this
board it when it comes out of the spring
and does it very if i do a three five
six times in a row it's not a
twenty thousand dollar
spring dot
so
it likely to vary
and the way i'm going to go to the is as
follows
if i showed an object
brought it up
that is the maximum value that it can go
olha
equals ninety degrees
and a sign of all five one
and the heights
is dangerous creat departed bite to eat
in other words
if i measure the hike turkey partial to
the predicament
and you can read about
for me you will see how i'm asking you
to do that
and we can calculate
the heroes quick
for the first thing i want to do
is to shoot up directly
and
how are you going to help me
compelled to tell me how hard it is
that goes
easier than you think
the pop art
removed this
the pump parts all for this
stick
three meters the pulp mark
it's very top markets reviews
and all i wanted to tell me whether this
very much above
we gave much below
and then to estimate that came out
and then we'll make a guess
and i'll do it twice
when you're ready
make sure you can distinguish between
above and below makes a big difference
okay
three to while zero
okay ordered higher or lower
follows
there we agree
let's say five centimeters lights
we're going to allow for non certainty
i'll do it again
wanna see how well it with the juices
well zero
lower
source then sent me this five
centimeters higher
so we'll take seven
so we'll make seven then we'll have to
allow for an uncertainty
so h max
is about three
point all seven
i have deleted morning twenty times
and there were times that the heights
different to buy more than ten seven
means sometimes even fifteen senators
i'd therefore
would feel most comfortable confortable
if you are only a month for a complete
of fifteen centimeters
in that hot
remember once we start shooting at
thirty degrees there's no way that we
can evaluate the velocity anymore we
have to just take its value
at face value this is the way we've
measured the zero and that's it
defeated five percent ever
five percent
so what now is b zero scraped
well that's easy to calculate now
the zero squared
equals
three point oh seven
fine still
finds nine point eight
all my calculate the wheels off that's a
detail
three point or something
times too
times nine point eight
that is sixty
would want to have not like it too
check that
sixty point one seven
was in a row five percent
that is never
so you might as well make the sixty
point two
would you please confirm that that i
didn't make a mistake
three point oh seven
is age max
i'm idle deployed by two
by nine point nine
is sixty point two
two five percent ever and a five percent
ever
using the three
is meter squared
per second square
i don't care what the general race
because if we go to measure olis all
they need is the zero square
and if you would call i'm going to
calculate what the height will be at the
various angles all you need to be heroes
so i'm not even interested in detail
i'll just stick to p zero squared
andy zero squared
will have exactly the same uncertainty
right uncertainty a five percent
because it comes immediately from h is
not going to change that
okay sir so much
forty uncertainty indeed zero script
now i'm going to set the angle
at forty five degrees
how accurately can i do that
i don't think i can do it any better
than one degree
applying to do the best i can
i can't really guarantee you that i'm
back here to one degree
tune-up comes the question
what happens with this fine
alter
to opt out
with regard to measure alas
what happens with the final
to all time
the final ninety degrees
is one point zero zero zero zero
but what would be just fine
of eighty eight degrees
that is the value that i cannot excludes
if i'm off by one degree
and that value is or points
nine
passport
that is so close to one
that it is only off by all point six
percent
or point below six percent
and that is slow
compared to five percent
forget its forget the ever in all four
we can't completely forget it there's a
reason for that
when all fine
it's forty-five degrees
and to all five ninety degrees
and assign curve goes like this at
ninety degrees is almost fraction
so even if you often and will buy a
little bit you still very close to one
that's the reason
so all we have to worry about the
students certainty
indeed zero screech
and so now comes word that prediction
i'm going to make a prediction out
for forty five degrees
alas
equals
v zero scratched
we have that that is sixteen point two
and we have decided to all things one
then we divide by
nine-point dates
thirty six point one four leaders
with an uncertain people fight strength
right to protection to complete your
script
and so that is an uncertainty orpheum
centimeters actually thirty-one
sentences
this is my prediction
when angle
forty five degrees
his will
only holds if there is no ever ek
what is the average is negligible
and of course
equally important
that that spring gone
when the balkans out
velocity square is indeed within the
range that we have assumed
doesn't have a bad day
and good days there's no way i'm dike
unchecked it anymore
all right
so we're going to watch v
point six one four
it is one leader two leaders three meter
for me to fight leader
six meter
six point one four
long four
fourteen sending me this were here
and then on the local whenever
off about
thirty centimeters you don't do that
right
that is correct
forty five degrees for thirty cent
leader
uncertainty
as all the way up here
and then the next one
roughly thirty c
that's where
evil calculations make sense
that's where the all stupid
now i would like
you to come here if you don't mind
spent here
and the woman that that bullets
pointer finger dates
don't do it before a shilpa just
affirmation
and then we'll hope for the best
governor of his life
where what happened was that ball that i
had
that within my pockets
always here
so i'm going to start it now to the best
i can at forty five degrees
and
to academics who did any further
maximum possible
just
really
you look at me who bear goes fast
wall europe
we did we get there
that's fantastic
isn't that amazing
we see how important it is if you have a
uncertainties in your measurements
in high school you would have said it
has to get there
bowman
it has an error
and here i have to be taken into account
read my ball biter
eleven u
okay
you can sit down all you did graded work
just because you were there
now
i wonder
what happens if i
five of the
bullets
thirty degrees
flavor you would have thirty degrees
then
the zero square is the same i don't have
to worry about that idle
however
i cannot be certain
about the angle
for better than one degree
so you will see
that come on out
don't be decadent
here we have an air or bullet point two
oh six percent
because of these one degree
possible one degree offset
that's just ignore this ever to
bad is risky
that his risk email
because the sign of sixty degrees steps
which would you please
the sign off sixty degrees
i think it'll point eight six six that's
right
but the sign
or fifty eighty degrees
which is possible if i'm wrong degree
holder
is or forty eight four eight
and back these substantially lower
and therefore
i must
allow
for an uncertainty
in this time of the angle
by roughly
old maybe something like seventeen or
eighteen units point or what is this
difference
what or important
you want to check checked with this line
of sixty two degrees if you will see
that that is about
this much
higher than this
so we must allow for these error
and that is an error
riches
by no means
negligible anymore
no point here
there's an error which is eighteen
divided by eight six six
that is a two percent their work
so now we've needed all of the southern
wasn't two-percent error
in the signed off to a fire
even though
there's only one degree uncertainty in
the angle
and the reason this at this time curve
is like so
source mall angle change hue makes no
difference
but the small angle change he makes a
lot of different and that's the reason
you can see that it is the slope
of the swine curve
that gives you a much larger error if
you recall
teeny weeny little bit
so now we are ready to make a prediction
view comes the prediction
alas
no four thirty degrees
so i have to go through
the heroes create i have that
sixteen point three
and that i have to multiply by the
scientific to ul font
that is the signed all
sixty
multiplied
and then i think i have to divide by
g_m_'s rights
nine-point its
and i point five point three one
auto minus
not
two-percent error in the sign
to all fine
five percent ever in b zero script
that gives me i can't help it
seven percent at work
so i have a seven percent uncertainty
multiply by point two oh seven
so i cannot trustees any better and
thirty seven centimeters
and so now i'm going to put two markers
outs
five meters and thirty-one senators
this is the five meter mark
that he wants any new news
and i a loaf of thirty seven centimeters
either side
let's hear it
and thirty seven centimeters decides
is here
place at the end of the thirty degrees
aku
we need
movement forward
the year
stay out of the fire alarm
and when bullets
jump on its jump on it
okay
everything under control
five min choi market like five meters
three one that looks about okay
and now i have to
change the angle to thirty degrees
okay as close as i can do it
okay
la
well
hit the jackpot
incredible
what you can all you know
and successfully
you could say perhaps you have been a
little bit too conservative
on you errors and i admit that
but believe me when i get this morning
despite six times that the aryan v zero
was quite substantial beehive
differences were sometimes fifteen
centimetres
and so i have no choice
but it looks like we were a bit on the
conservative sites
suppose no i repeat his experiment
at sixty degrees
what will change
what will change
brillo exchange
no because the sign of conduct twenty
degrees is the same
as the sign
sixty degrees
you have to also u
final sixty is the same as the sign
humble twenty
if you allow for an uncertainty
while negril he decides
you'll find exactly the same numbers
because of the senatorial assigned
career
so again we're all by two percent
no difference
and so this prediction is unchanged
forever i want to ask you one question
to see whether you are
householders or half asleep
at thirty degrees
your soul is
at sixty degrees giving it the same
initial speed
you will see this
it will have to make you within the
uncertainty overworked measurement at
the same location
it will of course
of course go much higher
you can calculate that
because you will have to use this forty
creation for the heights
and that goes with the sign of all time
so i hope all part of sixty degrees is
way harder than thirty degrees
now comes the question
real best trajectory
take longer
then this long
or will they did the same amount of time
which for the same amount of time
which for longer
which was shorter
i am happy with
concept of fingers and unhappy with
another sample fingers
want is the horizontal velocity
of the cold war
when it takes off
if the velocity is the same
in both cases
and receipt that this horizontal
component
is where you are doing than the total on
and if they traveled the same distance
trip must
take longer
because it's the horizontal component in
the actual rection
the germans how long it will take
to go from here
to bear
suppose i show it
straight-up how long you think it will
take to get here
that has no worries a little component
think about these this project you will
take longer
but it ends up at the same
all right
number three
you come here
so i don't have to change the marcus
they're all perfect
provided that
nature's whittington replete with itself
sixty degrees
will go where i worked
but it will go as well
to hit
within the same way
copyrights
thank you very much wonderful walk
maybe body uncertainties were not so
we were both looking here is the jek
fault
comfortably within the error
close to this one
so i'm quite happy that either
took the uncertainties the way i did
it can be recovered the ball that
someone see it
they cult-like
all right
now we will
enter a different part
this lecture
which is actually
very
very set point
you know that people in africa
chilled monkeys
there's a monkey unit three
very happy
and here is a bumper
who never took eight oh one
and
he has a
a gun which is the golden bull gone
uh... on
and things that go on
right at the
he shoots it was a certain velocity
gullible
let this be
speed
zero
the horizontal components
you're going to see that again and again
the hero called or pot
and a vertical components
equals v zero
stinar
bisbee
my increasing value white
bisbee might increase in value
this term
gullible
distance gold gone
is really not first class
thank goodness
and so
when the hunter shoots this cold war
this happens
and it ends up here
appointed
lucky
monkey
so far
now
it is very tragic the true
that when the monkey sees the flesh of
the gun
it let's go
and now comes the question
is the monkey safe
or
it is the last day optimum
i asked the following question
this would be the trajectory
with no gravity
and this is the project three
with gratitude we can both agree on that
at us at the moment can you mom
let's assume
the global would have been here
without gravity
then that i know exactly where these
with gravity
it must be exactly here
because
the exposition
exp one
is the same because the horizontal
velocities the same
that's independent
or whether there's gravity or not
there is no acceleration in the next
election
and so
they are both exactly at the same
exposition
is this difference
well that is the difference between
equation with gravity and without
gravity
and why
as a function of time
you can look at a greater number
three there if you can still see it
equals v zero y which is the zero sign
off on that
frankly
minus
one hops
g transcript
well
if there is no gravity this term doesn't
exist
so that's the straight line
was gravity it's the same thing but you
have to subtract this
therefore this distance is one-half
g
wild
square
at a distance
this cortisol all abide it tomorrow
now comes a time
that the cold war
it's point p
when its position
is extend to
time here
is key to
that means if there had been no gravity
the gold what would have been there
you must have the same position in acts
at these catastrophic moments
so what now
is the
distance between the monkey
and the global
the distance between the two projectors
one trajectory no gravity ditto with
gravity
this distance
equals one-half
ki
square for that same reason
and we all know
that if the monkey
at time t equals zero let go
bedding t two seconds
it will have fallen exactly over this
things while half
to screen
exactly
couldn't be more tragic
and he will be killed
you may save well
yeah but you have manipulated
the speedo background
just so nicely
i can shoot that was a higher speed at
the same angle all pod
and
the trajectory would be this
and the monkey would be killed by
i can do it was a lot of speech
and the monkey would be to yet it's
independent of the speed of the boats
always depart here
always exactly the distance that the
monkey falls in that time
however
if this speech is very low
that hits the ground before the monkey
hits the ground ground ok monkeys
so diol
only thing that is very very critical is
all-star
must be precisely
at the monkey
that's not the case
the monkey
we'll be safe
well before any real witnessed this
classic and rather tragic
drama
i want to look at this
form a somewhat different point of view
namely point a point of view of the
monkey
the monkey sits there
looks at the gone
and the gold balkans
to him
and i will put them both
in a room
just an elevator
an elevator isn't free fall and they
don't even know that
they both full thursday acceleration
you're demanding
here
the velocity
of that bullets
is the zero
and soda monkey will see that bullets
coast blank
there's no such thing as an art
it boastful in this photograph index
falling elevator
welcomes
the monkey
happens to be the very intelligent
monkey
and among confessed to himself how long
do i have to live
and the monkey make the following
calculation
depicted candidly
and indicates
then the monkey cells are hot
it's group called the career
was a clear
so from the monkey point of view
time for the kill
will be described wrote
open square
quiz h career
divided by the zero
that's how many seconds he has to make
would you people are also quite smart
and you look at this diagram
and use it
no way
if this distances d
bended
to reach this point
is the zero cosign on fire
in other words the time that it takes
for the assault ject
to reach this value x
sold for twenty six one hundred m_i_t_
students
pre-trial
equals
divided by
the zero
co-signed all fine
but one of the coastline double clock
that is d divided by the square root
of the script
was eight square
so i can replace this co-sign all fine
buddy
divided by the screws
so i can replace the spokesman also up
viji
divided by discouraged
and one p
exactly on the amount of time
at the monkey estimate it better be that
way
because this could not depend on which
reference frame
you work in the following reference
frame
for that matter
reference frame twenty six one hundred
one key will be placed
about three leaders above the
we all know that it takes about four
point eight seconds we've done any
experiments three meters
fixable or point eight seconds
soda whole thing will go very fast we
were going to put the monkey up there
i want you to foresee the trajectory of
the gold ball before we bring the monkey
in the it is already so painful forties
monkey
you don't want him to
free experience was going to happen
so we will do this
in the absence of the monkey
and we will let you i will let you know
c
rapidly
the trajectory
of that pool it will be
while zero
so it will get somewhere here
at that point p
so when you're going to see the drama in
action
this is where
the monkey real reach when the two
you can imagine
that's this is a very painful day for
the monkey
i'm going to get the monkey
behind here and
hope that you will
basam respectable his name is robert
and
it may take me a minute
here is a lot of
high-quality
i thought it was appropriate to change
forty location
cardozo
on monkey
pumps too often
but when i do it i'd like to do with
style
you is what works
and we're going to put romanov
roberts
has
in his head
a metal plates
so let's when reactivated
electro magnets
weak and sticking on there
and when we take the current off
robert willful
so this is the activation of the
electoral
here we go
i can see what what is nervous
and you can't blame him
it is not the greatest day
his life
but by the way i wanted to know
we we are not
cruelty
he's read a bulletproof vest
i can likened
deal with the shaking all over his body
their interest
roberts
don't let go yet
okay let me show you what's important
that you know
that we have done everything we can
through eight is gone
as accurately as we can have robert
wal-mart
don't let go yet
lurk first got to go out and all that
alcohol that world works out
it happens always was what works
okay just promise me
that he will not
that go with that
when i
octagon if i can find to be
school performance here
electric circuits
states over
and all the current will be disconnected
the don't that's fine
hi even i'm nervous i'll admit it you
know this is a terrible thing to do it
terrible thing to do
loan zero
have
werman
ceo private
