Archive for the ‘Linear Equation’ 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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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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Could you return Andy Murray’s serve?

January 29, 2015

 

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

TOMAS BERDYCH

TOMAS BERDYCH

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

Andy Murray

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:

1. Top 10 Tennis Serve Speed

 

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

2a Mathspig Tennis Serve 2 maths

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!!!!

Tennis pythagoras

 

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:

3 Drop test 2

4 Reaction Time Chart 2

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:

mathspoig 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?

5a Mathspig Andy Murray

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!

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How to pig out and save the planet

January 2, 2015

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:

Picture 1

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:

Picture 3

Mathspig Kilo carbon dioxide released per kg FAT

 Picture 3

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:

Mathpig Carbon Footprint by pig out

 

Picture 3

 

We can Pig Out and Save the Planet:

Pig Out Australia 2

 

Picture 3

Pig Out UK 2

 

Picture 3

 

Pig Out USA

 

Picture 3

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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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Outdoor Maths Adventures: Middle School

June 30, 2014

 

 

Outdoor maths middle school 1 mathspig

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!

 

Outdoor Maths Middle School 2 Mathspig

McGill Uni link here.

Outdoor Maths MIddle School 3 Mathspig

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

Outdoor Maths Middle School 4 mathspig

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

Outdoor Maths Middle School 5 Mathspig

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

Outdoor Maths Middle school 6 Mathspig

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.

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4. Build a Creepy Crabmobile

October 3, 2013

Why build a crabmobile?

Crabster CR200

Because working underwater involves huge pressures. To keep it simple the best pressure unit to use is Atmospheres.

 At sea level ( 0 m) the pressure is 1 Atmosphere (atmos).

…………………………………………………………………………….

Every 10 m depth adds 1 atmos pressure.

At 10 m the pressure on your lungs is 2 atmos ie double sea level.

At 20 m the pressure on your lungs is 3 atmos ie triple sea level.

…………………………………………………………………………….

How strong are Your Lungs?

 …………………………………………………………………………….

 You breath air at 1 atmos pressure in and out.

According to The Institute for Structure and Nuclear Astrophysics, Indiana

your lungs only have a capacity:

 …………………………. ± 0.03 Atmos

 …………………………………………………………………………….

hose calc If this comes as a surprise, try it. Try breathing through a hose of, say, 50 cm. 

You will find it quite difficult.

 …………………………………………………………………………….

SCUBA DIVING

 …………………………………………………………………………….

The regulator on the SCUBA tanks feeds you air at a pressure experienced at that depth.

ie. At 10 m you breathe air at 2 atmos pressure

     At 20 m you breathe air at 3 atmos

Pressure at each depth can be calculated using this equation:

 

Pressure formula

 

But here is the Problem:

scuba diver

 …………………………………………………………………………….

AT 30 m ( 100 ft) the disorientation of Nitrogen Narcosis begins.

It’s caused by too much nitrogen dissolving in the blood under pressure.

At 50 m (165 ft) Slowed response. Laughter.

AT 66 m  (217 ft) oxygen toxicity kicks in.

At 70 m (230 ft) Flawed judgment. Hallucinations.

At 90 m stupefaction.

 

pressure chart 2

 

But if you surface too quickly the nitrogen bubbles out in your blood and gives you the bends so called because it is soooo painful.

Ahhhhhh!

……………………………………………………………

Introducing the Crabster CR 200


crabster_cr200_3

According to Gizmodo, one problem with conventional ROVs – Remotely Controlled Vehicles – is their propellers kick up silt from the sea floor, and their engines struggle in strong currents. But this new underwater explorer sidesteps both of these problems by skittering around the sea floor like a crab.

techno crab

CRABSTER CR 200, developed by a team at the Korean Institute of Ocean Science and Technology (KIOST), can survey shipwrecks and collect data for research. It has 4 pilots. One for the walking and posture. One for the manipulators, cameras and lights. One for the sonar and other scanning equipment. One navigator. This is some creepy crab.

How much pressure can the Crabster withstand?

At 240 m:

p = 0.1 d + 1 = 0.1 x 240 + 1 = 24 + 1 =  25 atmos

Wow! That is  25 times more than sea level.