Galileo’s Concept of Projectile Motion

1. Galileo’s Concept of Projectile Motion By: Chad Hainley And Billy Jack

2. 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)!

3. Galileo first discovered that the curved path followed by a projectile is a parabola, and that projectile motion is therefore uniform.

4. 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!).

5. 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.

6. 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.

7. 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.

8. Just a Few Uses of Projectile Motion

9. Now it is time for the discovery of uniform projectile motion to help you to continue to rule your country with an iron-fist!

10. 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: V(x)=Cos(30)*50 V(x)=43.3 m/s V(y)=Sin(30)*50 V(y)=25 m/s Time in the air: a = (vyf – vyi)/t -9.8 = (-25– 25)/t t = 5.10 s Distance Traveled: vx = (xf – xi)/t 43.3 = xf/5.10 xf = 220.83 m

11. 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)!