Speed and Mass of a Dodge Ball: Dodgeball: A True Underdog Story
An educational, fair use website
Abstract
The purpose of this is to analyze the 2004 movie, Dodgeball: A True Underdog Story.
Introduction
Movie Synopsis
Peter Lafleur (Vince Vaughn) is the owner of Average Joe's Gym, the rundown workout facility compared to the highly macho GloboGym across the street, founded by White Goodman (Ben Stiller). Lafleur hasn't collected membership fees from his members and therefore has landed himself in a high debt. GloboGym decides to buy out Average Joe's with the help of a bank attorney, Kate Veach (Christine Taylor). Lafleur has to somehow acquire $50,000 in order to keep his gym.
Average Joe's is made up of 5 members in total: a high school klutz with a dream of becoming a cheerleader, a man who believes he is a pirate, a man with an unloving mail-order wife, a cocky know-it-all who doesn't seem to know much, and a dim-witted young man. Together, they come across an ad for a dodgeball tournament that awards $50,000 to the national winner.After being disgusted by Goodman's egotisical personality, Kate decides to join Average Joe's team, as she had played eight years of softball. With his spy activity, Goodman finds out about the tournament, and enters his gym in the competition as well.
It is clear that the social rejects in Average Joe's Gym would not stand a chance against the likes of Goodman and his band of buff bodies. However, Patches O' Houlihan, a dodgeball all-star champion, comes along and becomes Average Joe's coach. He trains the team with harsh routines, which included dodging moving traffic on a highway and dodging wrenches thrown at them. With luck, determination, and focus, the misfits win the tournament and end up owning GloboGym. This is a cinderella story with a dream come true ending- except with dodgeballs.
History of the Game
Dodgeball is a sport (more often a game) that is played in a physical education class in elementary school. Nowadays, the game has been abandoned by schools because of ongoing controversy. Advocates say that dodgeball allows for a "safer" outlet for letting out anger. Critics disagree and say that bullies can use the game to pick on and abuse less popular and unathletic classmates.
Rules of the Game
There are two teams, 6 players on each side, and 6 rubber balls. The object of the game is to eliminate players on the opposing team by hitting them with a rubber ball. A team is declared a winner once all the players of a team are eliminated. Along the way, players must also dodge the balls being thrown at them from the opposing team. If you catch a ball thrown at you before it hits the ground, the thrower is out and you get to bring another player back in. In the training documentary seen in the movie, there are five main rules of dodgeball: Dodge, Duck, Dip, Dive, and Dodge.
Analysis
Sudden Death- Velocity of the Dodgeball
The first scene analyzed was the Sudden Death match between Lafleur and Goodman. Both players were each provided with a silver rubber ball and were confined in a triangle on their side of the court. Lafleur blindfolds himself with Patches' old lucky hankerchief and is playing in his memory, as shown in the following picture:
In the movie, Lafleur dodges Goodman's throw as if he were in the Matrix and fires back with his own spectacular throw.
The ball hits Goodman at the position where he is standing in the screen capture. According to Internet sources, Vince Vaughn is 6'5'' (1.96 m). I scaled his height as he appeared on my television screen using a ruler to determine the distance Lafleur's ball traveled before it hit Goodman:
1.96 m = 3.0 inches
→ 4.74 m = 7.25 inches
To determine the time it takes for the ball to hit Goodman, I used Windows Media Player Classic and measured the frame rate. Standard frame rate for a movie on the media player is 24 frames per second. It took 11 frames for the ball to hit Goodman in the face. The time it takes, therefore, is 0.458 seconds.
So how fast was Lafleur's throw? I calculated that using the equation:
v = s/t
v = 4.74 m/0.458 seconds
v = 10.35 m/s
Mass of a Dodgeball
After being pummeled by the ball, Goodman makes an unrealistic fall- he lands on the yellow line of words at the back of the court (refer to the previous screen capture). Using the same capture, I again used the previous scale to measure the distance he was flown backwards.
1.96 m = 3.0 inches
→ 4.90 m = 7.5 inches
If he flew that far back, the mass of the ball must have been a fairly large number. To calculate the mass of the ball, I used the concept of conservation of momentum (linear, not angular). To get the time it took for Goodman to make the complete fall, I again measured the frame rate. It took 73 frames until he came to rest. If there are 24 frames in a second, the time is then calculated as 3.04 seconds. However, the fall was presented in slow motion. Therefore, we can estimate that the real time of fall is about half and is 1.52 seconds. With this, I figured out the initial velocity of Goodman at the moment he was hit by the ball:
vf2 = v02 + 2as
0 = v02 + 2as
−v02 = 2(Δv/t)s
v0 = 2 s/t
v0 = 2(4.90 m)/(1.52 seconds)
v0 = 6.45 m/s
Now, for the conservation of momentum part. Initially, there's only the mass of the ball (mb) and its velocity (vb). Final momentum is just Goodman's mass (mG) and velocity (vG) as he is "flying" backwards. I estimated that Goodman had a mass of 80 kg:
p0 = pf
mbvb = mGvG
mb(10.35 m/s) = 80kg (6.45 m/s)
mb = 50 kg
That is an incredibly large and obviously inaccurate mass for a rubber dodgeball.
Conclusion
From all the measurements and calculations, it's easy to deduce that the movie exaggerated the effects of a real dodgeball collision. In reality, Goodman would not have fallen back nearly 5 meters. What the movie does is bring justice to Average Joe's- the true underdogs in comparison to the macho GloboGym. We can't help but cheer for the Joe's and scorn Goodman.
Jennifer Leong -- 2006
External links to this page:
- The Physics of Dodgeball, i love this world, 19 October 2006