Archive for the ‘Simultaneous Equations’ Category

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The Terrifying Maths of Running from a Bear … Metric Units

July 17, 2017

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.

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The Terrifying Math of Running from a Bear … USA Units

July 17, 2017

USA UNITS below. METRIC UNITS here.

BEAR STATISTICS

Grizzly Bear

Weight:  550 lb        

Height:  8’ 2”   

Top Speed: 35 mph  =   51 ft/s    

Brown Bear

Weight:  1,500 lb       

Height:  8’ 2”              

Top Speed: 22 mph  =  32 ft/s     

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

Usain Bolt:

Top speed: 27 mph  =   40 ft/s     

Bears are not dangerous:

………………………………………………………………………


In fact, more Americans die each year from choking on their own vomit than are killed by bears.

More death stats here

Nevertheless, bears are very fast. So you can see why Park Rangers offer the following advice:

More information at Mountain Nature.

The reason for waiting until the bear is 15 ft away is to make sure the spray doesn’t disperse in the air. If the Pepper Spray is too spread out it will not stop the bear.

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

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Fire Fighters Need Maths

October 22, 2015

emergency-ABC Radio Announcement

Black-Saturday-Bushfire-300x168

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. erickson-aircrane-elvis

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

Here is something you may not realise:

fire fighters need maths

And the maths they need is

MIDDLE SCHOOL MATHS.

Fire fighter running up mountain vector 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

fire-chair pixabay

METRIC UNITS

On 7th 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 S(Fire Truck Speed) in m/sec and kph.
  2. Fill in this equation where  d  (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.

Picture 1

fire fighters need maths

USA UNITS

On 7th 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.

Picture 1

ANS Q 7 METRIC fire fighters need maths ANS Q 7 USA UNITS

Roni butt on fireWORKSHEETS

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.

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Dangerous Maths 3: Shark Attack

July 31, 2015

Aussie Pro surfer, Mick Fanning, grabbed world attention when he was attacked by a shark in the Fanning J-Bay Open, South Africa on Sunday 19 July, 2015. Fanning was knocked off his board and forced to fight for his life. He survived. News.com

1  Mick fanning shark attack

One shark expert suggested the shark was a young great white shark under 3.5 metres.

Would you survive a shark attack?

Let’s do the maths.

How fast can a shark swim?

According to the Smithsonian National Museum of Natural History:The torpedo shape of the great white is built for speed: up to 35 miles per hour (50 kilometers per hour). And then there are the teeth — 300 total in up to seven rows.

How fast can you swim?

According to Junior Olympic Games Qualifying Times 2015

For 13-14 yo 100m freestyle:

t girl = 1.15 or 75sec

t boy =1.10. Or 70 sec

Lets assure you are an average swimmer but highly motivated on seeing a shark:

t kid = 100 secs

So you can swim 100m in 100 sec. But will you survive??????

2 Shark Lesson Bluey's Beach NSW 2009 mathspig

 Surf Lesson Bluey’s Beach NSW 2009

We’re sooo tough in Australia! Shark, Smark! Whatever.

Picture from Daily Telegraph

Also according to the Smithsonian: Sharks can detect both the direction and amount of movement made by prey, even from as far as 820 feet (250 meters) away.

But there is hope as, according to the National Geographic Channel, Most shark attacks occur less than 100 feet or 30.5 m from the shore mainly around popular beaches in North America (especially Florida and Hawaii), Australia, and South Africa. 
3 Shark attack diagram  Mathspig

4 shark attack maths mathspig

Again we will assume that the swimmer is 30m offshore when he sees the shark fin 250m away. But this time we will have the world’s fastest swimmer. This time we are talking Dav vs Shark!!!!!!!!!

5 shark attack Maths mathspig

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Volcano Survivor 2: Mauna Loa Volcano, Hawaii, 1950

November 7, 2014
Once lava flows are established new RIVERLETS can run on top of the original lava flow at great speed.
Puu-Oo-USGS lava riverlets

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.

VL =   97 kph = 1.6 km per minute (k/min)

     =   60 mph

VH = 18 kph = 0.3 km/min

   = 11.2 mph (miles per hr )

GRAPH:

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

Mauna Loa Volcano Lava Flow 1950 2

 

SIMULTANEOUS EQNS:

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

Mathspig simultaneous Eqn 2

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Volcano Survivor 3: Mount Unzen, Japan, 1991.

November 7, 2014

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.

Mt Unzen  volcano-world

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.

Can you out run a pyroclastic cloud?

Mathspig simultaneous eqn 3

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

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Mathspig Solves Simultaneous Equations or Get the Hamster

March 4, 2013