Pumpkin Chunkin

  It is almost Halloween, the time of pumpkins and crazies who launch pumpkins with huge self built catapults.  This three decade old tradition raises funds for various groups and is due to happen the first weekend in November.

This event brings its followers in from all over the place.  I have friends who disappear for the weekend so they can go out to Delaware to watch.

There is some great math involved in this event from the parabolic projectile path to the time it takes for the pumpkin to travel across the field, etc.  Most people launch their pumpkins using some sort of air cannon to provide the force necessary to launch the object.

Lets start with finding the initial velocity by using the formula x*(k/m)^1/2 with m representing mass, k equals the spring constant, and x is distance in meters.  Since the pumpkin is being shot out of an object, you are dealing with projectile motion.  It is this motion which creates a wonderful parabolic shape. We can use the projectile motion equation d = (v^2osin(2theta))/g to find distance.  Add into this finding the time of the pumpkin's trip by using t = Vo sin(angle)

If they calculate the flight of the pumpkin without air resistance, then .  There is vertical and horizontal velocities, the angle of launch, and acceleration out of the cannon.  So you end up with the equation Vv= Vo sin(angle) and Vh =  Vo cos(angle).  A nice practical use for trigonometry.

If you add in drag, the equation changes to  drag = 1/2 * items density * speed^2 * area * drag coefficient.  Drag is what slows the object down and the area listed in the equation refers to the cross sectional area of the pumpkin which can be found using the equation pi * diamter^2/4.

Lots of cool math involved in shooting off a pumpkin. Yes it is mostly involves physics but its still the math involved when shooting a pumpkin.  So many things.  Just a fun fact, the pumpkin chuckers are still trying to hurl the pumpkin at least one mile but so far they have managed about 4,450 feet.

If you are interested in more math equations, just check out the internet for one of many articles with all the math equations needed to calculate just about anything to do with this event.  I chose just a few of the equations.  In addition, there are all sorts of plans to follow to build launchers.  Imagine having students build small versions of the launchers designed to launch those mini pumpkins.  Imagine having students follow up with the math to prove things. 

Let me know what you think!  Have a great day.  Tomorrow, I'm looking Halloween based math appropriate for use in the middle school or high school.