Transcript Galileo`s Concept of Projectile Motion

By: Chad Hainley
And
Billy Jack
 If you’re an average authoritative dictator, you wake up
each day wondering if it is the day that your oppressed
loving subjects rise up against you. Well today is that
day, and luckily you have a trebuchet, one giant
boulder, and the knowledge that projectile motion is
uniform (neglecting air resistance of course)!
 Galileo first discovered that the curved path followed
by a projectile is a parabola, and that projectile motion
is therefore uniform.
Projectile Motion Concept
 When an object is projected or thrown into the air it has a
certain magnitude and launch angle; these two
components combined are called the object’s directional
vector. This vector is made up of two component vectors;
one in the X direction and one in the Y direction. Once the
object has left whatever was exerting the force upon it,
gravity immediately starts affecting its velocity in the Y
direction; accelerating it downward at roughly 9.8 m/s2.
This force gives the projectile a parabolic motion in the air.
The velocity in the X direction however will remain
constant throughout its flight (negating air resistance of
course!).
Before Galileo’s Discovery
 Before Galileo made his discovery, it was thought by
Aristotle that there was either natural motion or
violent motion. In the example in order to make the
trebuchet launch the boulder, a force must act upon it
in order to cause and sustain violent motion in the
Aristotelian Universe.
 Yet, this view also states that once the force stops the
motion should stop as well. This clearly flawed logic
would mean that after the trebuchet was done putting
a force upon the boulder, instead of flying through the
air the boulder should simply fall to the ground.
Motion in the Aristotelian Universe
As soon as the string stopped touching the arrow, the arrow would
fall downwards since it no longer has a force acting upon it.
The Uses of Projectile Motion in
Everyday Life
 Thankfully the correct view of projectile motion was discovered
by Galileo, and it has impacted society in both the largest ways
by being the reason we all are able to use cell phones (by sending
satellites into space), and it also impacts society in little ways
such as throwing a football in one’s own back yard (which would
follow a parabolic flight path).
 Projectile motion has helped society through its use in sending
satellites and rockets into space, helping golfers figure out the
flight pattern of their golf balls over obstacles, as well as helping
egomaniacal leaders correctly wield trebuchets. All of the
various examples are just a fraction of how much of an impact
Galileo’s discovery of projectile motion has had on our society
and life would be extremely different without this valuable
discovery.
Just a Few Uses of Projectile
Motion
 Now it is time for the discovery of uniform projectile
motion to help you to continue to rule your country
with an iron-fist!
You Are Under Attack!
The rebels are ready to storm your castle and you know the following about your
trebuchet: The boulder is launched with an initial velocity of 50 m/s at an angle of
30o to the horizontal. What you need to figure out is: how far away will the boulder
land?
Resolve the vector:
Time in the air:
V(x)=Cos(30)*50
a = (v yf – v yi)/t
V(x)=43.3 m/s
-9.8 = (-25– 25)/t
V(y)=Sin(30)*50
t = 5.10 s
V(y)=25 m/s
Distance Traveled:
vx = (xf – xi)/t
43.3 = xf/5.10
xf = 220.83 m
Congratulations!
 Now all you have to do is wait until all those rebels are
220.83 meters away, and then they’ll learn exactly why
you spent the country’s entire treasury on a giant
catapult!
 You will remain the ruler of your land, and you can
thank your knowledge of Galileo’s concept of projectile
motion for that (as well as the giant trebuchet of
course)!