Projectile Motion: Medieval Edition

Catapults were originally created in the second half of the Third Age, first gaining huge international attention during the siege of Gondor by the allied troops of Mordor. Though the engineers of these catapults intended them to hurl large stones or other standard medieval weaponry, the troops of Mordor used the severed heads of prisoners to launch over the walls of the capital city, Gondor.

 Proof:

That was lovely, wasn't it?

As evidenced by the video above, the word catapult comes from the Greek words "kata" and "pultos" meaning "downward" and "shield", respectively. Katapultos came to mean "shield piercer" during the Middle Ages.

Materials: 

-2 6’ 2x4s

-2” and 2.5” wood screws

-8 mini-bungee cords

-2 6” bolts

-4 washers

-2 nuts for 6” bolts

-1” eye hooks

-spicy peanuts can

Procedure:

-2x4s were cut to desired lengths using circular saw.

-2x4 pieces were screwed together to form base and arm support structure.

-holes were drilled using half inch bit for axle and bump stop (bump stop requiring multiple holes for adjustability.

-arm was attached to structure.

-eye hooks were screwed into bottom of throwing arm and into sides of base.

-peanut can was attached to end of throwing arm.

- bungees attached to finish off the catapult.

*Special thanks to Robert for single-handedly building our group's catapult

**Even more thanks for building it to get disqualified 

If it hadn't been for a clause that our group neglected to adhere to during the creation of our catapult we could have been a serious contender for the launching competition in class.

Using the video analysis software from Vernier Software & Technology, we were able to graphically analyze and collect data from the launch of a tennis ball with our personal catapult. 

The original video looked like this:

Booooooring

But with a little time and magic you can make something cool like this:

And when you convert these in to some crafty graph-tys you get all this neat information:

Graph showing vertical position and velocity as a function of time. 

  Graph showing horizontal position and velocity as a function of time.

Range of projectile.

With this information we can calculate a few things:


What we know: 


Δx=5.194m
 Δy=.75m
Δt=.966s






Let's find the Launch Angle and Initial Velocity!


Δy=v_{y0t +}  ½at
.75=v_{y0(.966) +} ½(-9.8)(.966)
v_{y0=5.68 m/s}


Δx=vx0(t)
5.194=vx0(t)
Vx0=5.38 m/s


(5.38)² + (5.68)² = √61.1315 = 7.82 m/s
v0=7.82 m/s


tan-1=(5.68/5.38)=46.55°