Maths News: Volcano Survivor 2

Kilauea erupts in Hawaii MAY 2018.

The amazing maths of volcano eruptions.

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)

Can you out run a lava flow?

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 )

GRAPH:

How long will it take for the lava to catch you?

 

SIMULTANEOUS EQNS:

How long will it take for the lava to catch you?

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The Terrifying Maths of Running from a Bear … Metric Units

METRIC UNITS below. USA UNITS here.

BEAR STATISTICS

Grizzly Bear

Weight:   250kg

Height:   250cm

Top Speed: 56kph  =   16 m/sec

More bear stats here. 

Brown Bear

Weight:  680kg

Height:   250cm

Top Speed: 35kph  = 10m/s

More bear stats here.

Comparing these speeds to the fastest man on earth, Usain Bolt:

Usain Bolt:

Top speed: 243kph =   12m/s

So Usain Bolt could out run a Brown Bear but NOT a Grizzly!

Bears are NOT as dangerous as:

In fact more Americans die choking on their own vomit each year than a re killed by bears.

More death stats here.

But bears are very fast so Park Rangers recommend the following survival tactics:

More bear survival info here.

REF: Dog helps save hikers after grizzly chases them for 20 minutes here.

Fire Fighters Need Maths

-ABC Radio Announcement

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:

And the maths they need is

MIDDLE SCHOOL MATHS.

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:

Fire Fighter Math 1: Wildfire Algebra

METRIC UNITS

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?

1. Find S₁ (Fire Front Speed) and S₂ (Fire Truck Speed) in m/sec and kph.
2. Fill in this equation where  d₁   (distance of fire front from point on map) and d₂ (Distance of Fire Truck from the same point on a map)

         d₁ =   d₂   +   ………

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

USA UNITS

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?

1. Find S₁ (Fire Front Speed) and S₂ (Fire Truck Speed) in ft/sec and mph  
2. Fill in this equation where  d₁   (distance of fire front from point on map) and d₂ (Distance of Fire Truck from the same point on a map)

         d₁ =   d₂   +   ………

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

WORKSHEETS

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.

Could you return Andy Murray’s serve?

 

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

TOMAS BERDYCH

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

Andy Murray

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.

Would you be able to return the serve of a top tennis player?

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?

BUT … BUT … BUT … 

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:

How fast is YOUR reaction time?

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:

1. The meter rule Method:

See details at Top End Sports Website.

2. Online Reaction Time Test

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.

Could you return Andy Murray’s serve? 

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!

How to pig out and save the planet

Aussie physicist and TV present – that does sound like an oxymoron – Reuben Meerman (A meer man after all. Old joke) had an article published in the BJM (British Medical Journal) with Andrew Brown describing where fat goes when you lose it.

When you burn fat which is a triglyceride or a three-pronged hydrocarbon the formula is:

You breath out the FAT as CO2 and H2O.

BUT:

Oxidizing 10 kilos of human fat requires inhaling 29 kilos of oxygen to produce 28 kilos of carbon dioxide and 11 kilos of water. You can check out how much carbon dioxide you add to the atmosphere when you diet in the following graph:

 

When you lose weight you add carbon dioxide to the atmosphere, but when you gain weight you take carbon dioxide out of the air. Your carbon footprint from Time for Change blog (See table below) can be neutralised if you put on the following weight:

 

 

We can Pig Out and Save the Planet:

 

 

 

 

Volcano Survivor 2: Mauna Loa Volcano, Hawaii, 1950

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)

Can you out run a lava flow?

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 )

GRAPH:

How long will it take for the lava to catch you?

 

SIMULTANEOUS EQNS:

How long will it take for the lava to catch you?

Outdoor Maths Adventures: Middle School

 

 

Lego Man soccer fields will vary in size depending on the height of each player picked by each student. This does your head in. It is really challenging maths!

 

McGill Uni link here.

Don’t forget to throw in Mathspig’s lame protractor jokes.

You’ll find full calculations at the Maths is Fun blog.

You’ll find more fab outdoor junior and middle school maths activities at the terrific Maths and Movement blog.

Some students will discover their co-ordinate point is not on the grid. Students should then work out that they will need a different scale for the y-axis. You can get more inspiration at the Stand Again blog.