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**The following maths is suitable for Year 9+**

**but can be presented to lower grades just to show**

**maths is cool!**

Just another WordPress.com weblog

………………………………………………

**The following maths is suitable for Year 9+**

**but can be presented to lower grades just to show**

**maths is cool!**

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Black Saturday Bush Fires Australia

The Fire Season in Australia arrives suddenly. The frightening warning (above) can be heard on the national broadcaster as fires spring up around Australia. It seems no time at all since Aussie fire fighters were helping fight fires in California. Now they’re back. Elvis, The Aircrane, returns form the US for another tour of duty in Victoria.

Aircrane, Elvis, returns to fight bush fires in Australia. Herald Sun

Here is something you may not realise:

You can check out a typical Fire Fighter Maths Curriculum here. The significance of the Fire Fighter Maths is that the numbers are shocking. You can look at a wildfire on TV, but when you calculate how much time you have to escape, the answer is truly terrifying.

So here is a Fire Fighter Maths problem from one of Mathspig’s Middle School Worksheets titled:

**On 7 ^{th} February 2009 a bushfire began in Victoria Australia that killed 173 people, injured 414 people, destroyed 2,100 homes and displaced 7,562 people. Known as The Black Saturday Bushfires the fire front travelled at up to 600m per 30 seconds. The radiant heat produced was capable of killing people 400 meters away.**

Are fire fighters safe in such a fire? How much time do they get to escape the fire in a fire truck even if the fire front is 5 km away? We can do the math:

**Q 7: **You are a fire fighter in a fire truck when the wind hits the fire front at 120 km/hr. Suddenly, the fire front starts moving at 100 kph. You are, thankfully, in a fire truck but the wind and smoke haze makes driving the truck difficult. You can only make 80 kph along a straight road away from the fire (See pic above). The fire front is 5 km away. How long have you got before the fire front hits?

- Find S
_{1}(Fire Front Speed) and S_{2 }(Fire Truck Speed) in m/sec and kph. - Fill in this equation where d
_{1 }(distance of fire front from point on map) and d_{2}(Distance of Fire Truck from the same point on a map)

d_{1} = d_{2} + ………

3. Use the following equations to calculate the time t that you have before the flames hit.

**On 7 ^{th} February 2009 in The Black Saturday Bushfires the fire front travelled at to 656 yds per 30 seconds. The radiant heat produced was capable of killing people 437 yds away.**

Are fire fighters safe in such a fire? How much time do they get to escape the fire in a fire truck even if the fire front is 3.1 miles away? We can do the math. Answers below.

**Q 7: **You are a fire fighter in a fire truck when the wind hits the fire front at 75 mph. Suddenly, the fire front starts moving at 62 mph. You are, thankfully, in a fire truck but the wind and smoke haze makes driving the truck difficult. You can only make 50 mph along a straight road away from the fire (See pic above). The fire front is 3 miles away. How long have you got before the fire front hits?

- Find S
_{1}(Fire Front Speed) and S_{2 }(Fire Truck Speed) in ft/sec and mph - Fill in this equation where d
_{1 }(distance of fire front from point on map) and d_{2}(Distance of Fire Truck from the same point on a map)

d_{1} = d_{2} + ………

3. Use the following equations to calculate the time t that you have before the flames hit.

**Fire Fighter Math 1: Wildfire Algebra** You will find the worksheets in both METRIC & USA Units Here. Yes! There is a small fee. Mathspig and Roni the Rodent (left) have this very, very slow get rich quick scheme going. Ha!

Lesson Plan:

**Students discover that fire fighters need middle-school math. Students complete some warm-up exercises involving unit conversions (mph to ft/sec or kph to m/sec) without and with a calculator and then they simplify algebraic expressions and solve simultaneous equations. Students use this math to calculate real life fire front speeds that fire fighters have faced in Montana, USA and Victoria, Australia. The power of this math is that the calculations are based on the stories about and conditions faced by these real fire fighters. No lectures are needed on the danger of wildfires as the numbers speak for themselves.**

**Of course, tennis stars need maths … to count all that loot!!!!!!!**

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Mathspig is, like, soooooo excited. Tonight I’m gong to watch

**Tomas Berdych** (CZE) [7] play **Andy Murray** (GBR) [6] in the Semi-finals at the Australian Tennis Open.

**Some quick maths.**

Tomas Berdych is 1.96 METRES (6 FT. 5 IN.)

While Andy Murray is 1.91 METRES (6 FT. 3 IN.)

But, but, but …. Andy Murray, who is 26 years old and is 2 years younger than Berdych.

Here is the serve speed of the of the fastest recorded tennis serves in the world:

**How long would it take a tennis ball traveling at these speeds to reach the service line on the other side of the court?**

The tennis ball leaves the servers racket approx 3m above the baseline and travels along the hypotenuse to the service line. We must call in Pythagorus Theorem!!!!

You can calculate the time it takes a tennis ball to reach the service line for each player in the Top 10 Service Speeds List by using the simple v = x/t equation.

The big question is this:

You have to be able to move your racket before the ball arrives.

Can you do it mathspiggies?

You can calculate your reaction time by two methods:

See details at Top End Sports Website.

This is the best reaction time clock I’ve seen because it uses a traffic light system. Here is Mathspig’s reaction time:

Mathspigs reaction time was : 0.33 secs (see above)

So Mathspig would probably be hit on the head by a serve by Samuel Groth.

According to Wikipedia fastest service speed times for these two players are:

Andy Murray = 233 km/h (145 mph)

Tomas Berdych = 226.0 km/h (140.4 mph)

Tomas Berdych service speed just beats the fastest female tennis serve by Barbora Záhlavová-Strýcová at 225 km/h (140 mph).

Could Mathspig react in time to return Andy Murray’s server? Could you react in time?

Tomas Berdych’s serve would hit the line after 0.29 secs. Once again, I’d still be hit on the head. Ditto the top female tennis players.

Mathspig might lose if she played in the Aussie Tennis Open, but I’m a pig. I’d win serve GRUNT of the match. Ha!

In every volcano disaster movie from **Volcano** (1997) with Tommy Lee Jones to **Dante’s Peak** (1997) with Pierce Brosnan someone somewhere tries to out run a lava flow.

Is this possible? (See movie cliché busted by maths here.)

Now a lava flow from Hawaii’s Kilauea volcano is threatening tiny town of Pahoa, Hawaii. (below).

You will find excellent information about the Kilauea and other volcanoes at the

US Geological Survey here.

As the temperature of lava exceeds 1000^{0} C there are very few ways to stop lava. According to the Taylor Kate Brown SMH (10 SEPT 2014) options include:

Bombing

Blasting (it with cold water)

Barricading it

Or adding concrete.

Lava from Kilauea travels 17 yards per hour so the lava velocity is:

V_{L} = 17 yds/hour = 15.5 metres /hour

(See Vox.com)

Once lava flows are established new RIVERLETS can run on top of the original lava flow at great speed.

The fastest Lava flows recorded were in Hawaii in 1950 when Mauna Loa erupted. The lava traveled at 6 miles (10 kilometers) per hour through thick forest. But once the lava flows became established and good channels developed, the lava in the channels was flowing at up to 60 miles/hour (97 kph)

**You are 2 km from the volcano rim and start running.**

**V _{L} = 97 kph = 1.6 km per minute (k/min)**

** = 60 mph**

**V _{H} = 18 kph = 0.3 km/min**

** = 11.2 mph (miles per hr )**

One of the greatest dangers in a volcano eruption is not the lava flow, being hit by a lump of flying lava or rock, but by being choked by the fast moving scorching hot pyroclastic cloud.

In 1991 pyroclastic cloud blew out of the side of Mount Unzen in Japan. NASA has an excellent diagrams for such an event here.

According to the NASA website:

Highly mobile, these flows reach velocities of up to 400 kilometers (250 miles) per hour and can spread as far as 100 kilometers (60 miles) from the eruption point.

Here is what happened in 1991 when the pyroclastic cloud blew out of the side of Mount Unzen in Japan.