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Physics Doesn't Convict A Murderer After All : The Acquittal of Gordon Wood

This story takes place at The Gap, Sydney at a place called Suicide Point:-

The Gap, 188-. From the State Library of NSW 

Yesterday, after 3 years in gaol, Gordon Wood was acquitted of murder after he was originally found to have pushed his girlfriend, Caroline Byrne, off this popular suicide spot. In the original guilty verdict, the evidence relied on an expert witness called Rod Cross who subsequently wrote the book, "Evidence of Murder: How Physics Convicted a Killer." Previously, Cross had written books about the physics of tennis.

The physics of the Murder/Suicide/Misadventure is best found at mathspigs. In short, the cliff is 29m high and the body was found on the rock ledge below, 11.8m out from the cliff. This means the woman's velocity when she left the cliff was 4.85m/s. Since she couldn't have run off the cliff (there is a fence only 1.5m away from the edge), the woman was deemed to have been thrown off the edge and her partner went to gaol. Now this ruling has been overturned!

In the appeal, the judge ruled that to throw someone so far away from the edge of the cliff would endanger the life of the murderer. They figured this out by having some police officers throw others into a pool. Also, Gordon Wood was chaffeur for a famous rich man called Rene Rivkin. At the time of Byrne's death, Wood and Rivkin were being asked by the Australian Securities and Investment Commission (ASIC) about a suspicious fire and true ownership of shares in the company affected by the fire. In the murder appeal, the judge ruled the original jury should not have known about ASIC questioning Wood and Rivkin.

So, if she didn't run off the cliff, wasn't pushed, what now...?

Here is the trajectory of a body that mysteriously alighted from a cliff 29m high and landed 11.8m out from the base. Take the photo and use it with your class. CSI comes to maths!

Trajectory of a body that mysteriously alighted from a cliff 29m high and landed 11.8m out from the base.

 The equation of the parabola simplifies to:

y = - 5x²/24

If Byrne has taken her own life, she was running at 4.85m/s when she left the cliff. Could have Byrne reached the necessary velocity in 1.5m? This would require an acceleration of 7.84m/s².

Let's try it. That means you need to run 1.5m in 0.62s. Can data loggers help us accurately measure our rate of acceleration?

Your Mind's Eye - Spatial Abstraction

Everyone stand up.

On the count of 3, point to the location I am about to name. Don't be influenced by anyone, they could be wrong.

The canteen   1, 2, 3 ...
Everyone got this right, as it was visible from the room!

The bus stop   1, 2, 3 ...
Most got this right. It wasn't visible but it wasn't far away.

The local shopping mall   1, 2, 3 ...
A few more arms are pointing the wrong way, but consensus wins over.

Los Angeles   1, 2, 3 ...
Now, being in Australia, this location was a source of great debate.

After looking at Mercator and Peters projections of the planet, everyone agreed on a direction.

Now someone says, "We could go the other way around the globe."
Easy, point in the opposite direction to the last answer.

But then someone says, "We could dig through the earth."
I think, in the end, we actually did point towards L.A.

Giving Students Autonomy

Humans are motivated by Autonomy, a sense of having meaningful input and making a difference. So my Junior Maths Class' first task is to design, in groups of 3, the seating for their learning space. I like Dan Meyer's approach to patient problem solving so I will give the class as little information as possible and start with, 'What do we need to know?'

Of course, I have ideas I want the students to learn and use, so will try to subtly direct the task, notwithstanding past experiences where I have changed my approach based on ideas from the students. Anyway, here are some things I hope to achieve:

1. Measure accurately the room, desks and chairs. We are lucky to have two types of desks in the room.
2. Complete scale drawings of the floor plan and the desks, using grid paper or Google SketchUp.
3. List human considerations for interior design, such as group work, a break-out area, working space requirements and universal accessibility, such as wheelchair access.
4. Manipulate cut-outs to look at alternate arrangements.
5. Justify, in a 1 minute video, why the final design should be used by the whole class.
6. Evaluate all designs to reach a consensus on how our Maths Class will be organised.

Watch this space for progress reports on the task:

#1
"Is this for real?" asks one incredulous student. Says volumes about the curriculum!
Another barrier, of course, is the other people who share the room. Why would you give students a say over the arrangement of the room? On the other hand, we are interrupting other people's routines. (Is that a bad thing?)

Other than that, we are all having fun, figuring out "What we need to know" and "What skills we must use"