Archive for the ‘Year 9 Mathspig’ Category

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The Simple Maths of a Car used as a Weapon … METRIC units

February 3, 2017
NIce Truck Attack 2016 The Independent, UK

Nice Truck Attack 2016 The Independent, UK

Berlin Christmas Maraket Attack 2016, ABC

Berlin Christmas Maraket Attack 2016, ABC

Melbourne Car Attack 2017

Melbourne Car Attack 2017.

Cars (and trucks) have been used as weapons by drivers purposefully driving into crowds including:

2014: Saint-Jean-sur-Richelieu, Quebec

2014 : Jerusalem, Israel.

2016: Nice, France

2016: Berlin, Germany

2017: Jerusalem, Israel

2017: Melbourne, Australia.

What does the maths tell us?

Melbourne is Mathspig’s home town. The car attack killed, tragically, 6 people and injured many more. The question many seem to ask is:

Why can’t people get out of the way?

Look at the video below of the Melbourne car. It doesn’t appear to be going that fast. But the maths tells a different story. You need quite a distance between you and a car travelling at approx 60 kph to have enough time to run clear. (See calculations below)

How fast do you react?

We will set your reaction time at 0.4 sec. This allows time for you to react and turn. If you want to test your reaction time go here. But remember you have to turn as well.

How fast would you run?

According to the Telegraph, UK, the average human can run at 15.9 mph (25.6 kph) and the National Council of Strength and Fitness 15 mph (24.1kph), which Mathspig has rounded off to 25 kph.

car-used-as-weapon-1
car-used-as-weapon-2
car-used-as-weapon-3

How do you escape a car travelling at 60 kph towards you when you are less than 9 m away?

Jump upwards!

You might reduce the impact and even go over the roof.

car-used-as-weapon-4

car-used-as-weapon-5
car-used-as-weapon-6

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The Simple Math of a Car used as a Weapon … USA units

February 3, 2017
NIce Truck Attack 2016 The Independent, UK

Nice Truck Attack 2016 The Independent, UK

Berlin Christmas Maraket Attack 2016, ABC

Berlin Christmas Maraket Attack 2016, ABC

Melbourne Car Attack 2017

Melbourne Car Attack 2017.

Cars (and trucks) have been used as weapons by drivers purposefully driving into crowds including:

2014: Saint-Jean-sur-Richelieu, Quebec

2014 : Jerusalem, Israel.

2016: Nice, France

2016: Berlin, Germany

2017: Jerusalem, Israel

2017: Melbourne, Australia.

What does the math tell us?

Melbourne is Mathspig’s home town. The car attack killed, tragically, 6 people and injured many more. The question many seem to ask is:

Why can’t people get out of the way?

Look at the video below of the Melbourne car. It doesn’t appear to be going that fast. But the math tells a different story. You need quite a distance between you and a car travelling at approx 35 mph to have enough time to run clear. (See calculations below)

How fast do you react?

We will set your reaction time at 0.4 sec. This allows time for you to react and turn. If you want to test your reaction time go here. But remember you have to turn as well.

How fast would you run?

According to the National Council on Strength and Fitness the average human can run at the speed of 15 miles per hour for short periods of time.

car-used-as-weapon-7-usacar-used-as-weapon-8car-used-as-weapon-9

How do you escape a car travelling at 35 mph towards you when you are less than 27 ft away?

Jump upwards!

You might reduce the impact and even go over the roof.

car-used-as-weapon-10car-used-as-weapon-11car-used-as-weapon-12

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Tennis: Andy Murray is serving. How long have you got to return his serve?

January 19, 2017

 No. 1 UK tennis star Andy Murray is currently playing in the Melbourne Open. 

Mathspig often pops along to watch the tennis. 

andy-murray-serve-carine-06

Andy Murray’s Serve by Carineo6

Could you return Andy Murray’s serve? 

According to Wikipedia Andy Murray’s fastest serve speed is:

Andy Murray = 233 km/h (145 mph)

Keep in mind the fastest female tennis serve by Barbora Záhlavová-Strýcová is a very respectable 225 km/h (140 mph).

5a Mathspig Andy Murray

Go here to see why this simplified calculation works! 

Mathspig tested her reaction time here. TRY IT!

Mathspig’s best, best, best reaction time = O.33 sec

Could Mathspig return Andy Murray’s serve?

Nooooo!…………………………………………………………………….

I’d be hit in the head by a speeding tennis ball

before I even moved.

But I’m a pig. I got the best service GRUNT! Ha!

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Have Yourself a Mathsy Little Christmas

December 13, 2016

xmas-mathspig-2016

xmas-surprises

no-1………….no-2…….no-3….no-4………no-5………..

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Mad Mince Pie Maths

December 13, 2016

Mathematicians can make mountains out of mince pies, but in this case Dr Eugenia Cheng, who is Professor of Pure Mathematics at the University of Sheffield, UK, makes it look fun. The video clip includes some great Middle School Maths that you can eat.

mince-pie-diag

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Smoke Jumpers and their Amazing Wildfire Maths . . . . . . . . . . . . . . METRIC UNITS

December 5, 2016

mathspig-smoke-jumpers 

With wildfires in Texas and now Australia is facing the fire season, it is time to think about fire fighter maths.

mathspig-metric-units-fire-math

METRIC UNITS

Background Story

On 5th August 1949 Wag Dodge was dropped by parachute with 14 other fire fighters into Mann Gulch, a steep-sided gully in a Montana pine forest. Fire fighters who parachute in to put out small blazes started by lightening are called Smoke Jumpers. As they worked their way down the sides of the gully the breeze was blowing away from them. But the wind soon shifted. This produced an updraft, which increases the speed of the fire front. The 15 Smoke Jumpers turned and started running for their lives uphill.

HOW FAST CAN YOU RUN?

METRIC UNITS

Time Trial:

Mark out a 10 m course. Make 3 time trials.

t1 =

t2 =

t3=

Average your time:

tav = (t1 + t2 + t3)/ 3 =

Your Speed S = 10/tav = ……… m/sec

mathspig-firefirghter-maths-1

HOW FAST IS A GRASS FIRE?

This will, of course, vary depending on the wind speed. A typical grass fire in Australia in a flat area can travel at 20kph (up to 30 kph) in a gentle breeze.

Fire Front Speed Grass Fire

Fire Front Speed = 20 kph = 20 x1000/(60 x 60)

                               = 20 x 0.27777777 = 20 x 0.28 m/sec

                               = 5.6 m/sec

mathspig-firefighter-maths-2

CAN YOU OUT RUN A FIRE?

Average Running Speed Boy 13–14 yo = 3.0 m/sec

Average Running Speed Girl 13–14 yo = 2.4 m/sec

We’ll assume, boy or girl, that you are really motivated and can run away from the fire at top speed of 3.0 m/sec. Now calculate the distance you can run and the fire front moves in 10 secs intervals up to 1 minute.

mathspig-fire-fighter-table-1

This is not looking good. See more Firefighters Need Maths here.

We can do very accurate calculations using simultaneous equations. Wildfire Algebra: Detailed Worksheet using simultaneous equations and solutions  here.

NOW YOU ARE RUNNING UP HILL. WHAT HAPPENS?

We’ll assume, due to being motivated by having a fire licking your heels, that you can run at your top speed up hill for a short time, at least. But here is the problem.

Heat rises and so there is a Chimney Effect pushing the fire uphill. The rule of thumb used by fire fighters is:

Each 10º increase in slope, the fire front speed doubles.

mathspig-cfa-diag

mathspig-fire-fighter-table-2

Now you can calculate the distance travelled by the fire front up a slope at a 30º angle.

Don’t forget you can use the WEB 2.0 Calculator here.

mathspig-fire-fighter-table-3

Even at your top running speed, which is unlikely up a slope, you can run 180 m in 1 minute. In that time the forefront has moved 2688 m or 2.7 km.

It depends how far away you are from the fire front, but it seems you cannot out run this fire front.

Again we can do very accurate calculations using simultaneous equations.

See Firefighters Need Maths here.

Wildfire Algebra: Worksheet and solutions here.

CAN YOU OUT RUN A WILD FIRE?

High winds can turn a bush or forrest fire into a WILD FIRE with wind speeds up to 110 kph and temperatures up to 2000 °C, which can and does melt glass and cars.

The fire front speed doubles with every 10º, so speeds for the fire front can reach 220 kph, 330kph and up to 550kph.

20o-angle-mathspig-2

What happened to the Smoke Jumpers?

When the fire front changed direction Wag Dodge and 14 other Smoke Jumpers found themselves running for their lives up a steep slope. What did Wag do next?

ANS: Here’s the amazing thing. Wag realised he could not out run the fire at that point. So he stopped. Took off his back pack. Took out some MATCHES and lit a fire in the grassy patch in front of him. Just before the firewall hit he threw himself face down on the burnt patch. He survived. The other 14 firefighters did not.

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Smoke Jumpers and their Amazing Wildfire Maths . . . . . . . . . . . . . . USA UNITS

December 5, 2016

 

mathspig-smoke-jumpers 

With wildfires in Texas and now Australia is facing the fire season, it is time to think about fire fighter maths.

mathspig-usa-units-fire-math

 

USA UNITS

Background Story

On 5th August 1949 Wag Dodge was dropped by parachute with 14 other fire fighters into Mann Gulch, a steep-sided gully in a Montana pine forest. Fire fighters who parachute in to put out small blazes started by lightening are called Smoke Jumpers. As they worked their way down the sides of the gully the breeze was blowing away from them. But the wind soon shifted. This produced an updraft, which increases the speed of the fire front. The 15 Smoke Jumpers turned and started running for their lives uphill.

HOW FAST CAN YOU RUN?

USA UNITS

Time Trial:

Mark out a 30ft course. Make 3 time trials.

t1 =

t2 =

t3=

Average your time:

tav = (t1 + t2 + t3)/ 3 =

Your Speed S = 30/tav   ft/sec

mathspig-firefirghter-maths-1

HOW FAST IS A GRASS FIRE?

This will, of course,  vary depending on the wind speed. A typical grass fire in Australia in a flat area can travel at 12mph (up to 20mph) in a gentle breeze.

Fire Front Speed Grass Fire

Fire Front Speed = 12 mph = 12 x 5280/(60 x 60)

                           = 17.6 ft/sec

                           = 18 ft/sec

mathspig-firefighter-maths-2

CAN YOU OUT RUN A FIRE?

Average Running Speed Boy 13–14 yo = 10 ft/sec

Average Running Speed Girl 13–14 yo = 8 ft/sec

We’ll assume, boy or girl, that you are really motivated and can run away from the fire at top speed of 10 ft/sec and -Wow! – this is easy math. Now calculate the distance you can run and the fire front moves in 10 secs intervals up to 1 minute.

mathspig-fire-fighter-table-4

This is not looking good. See more Firefighters Need Maths here.

We can do very accurate calculations using simultaneous equations. Wildfire Algebra: Detailed Worksheet using simultaneous equations and solutions  here.

NOW YOU ARE RUNNING UP HILL. WHAT HAPPENS?

mathspig-cfa-diag-usa-units

We’ll assume, due to being motivated by having a fire licking your heels, that you can run at your top speed up hill for a short time, at least. But here is the problem.

Heat rises and so there is a Chimney Effect pushing the fire uphill. The rule of thumb used by fire fighters is:

Each 10º increase in slope, the fire front speed doubles.

mathspig-fire-fighter-table-5

Now you can calculate the distance travelled up a slope at a 30º angle.

Don’t forget you can use the WEB 2.0 Calculator here

mathspig-fire-fighter-table-6

Even at your top running speed, which is unlikely up a slope, you can run 1080 ft in 1 minute. In that time the forefront has moved 8640 ft or 1.6 miles. It depends how far away you are from the fire front when you start running, but it seems likely that you cannot out run this fire front.

Again we can do very accurate calculations using simultaneous equations.

See Firefighters Need Maths here.

Wildfire Algebra Worksheet and solutions  here.

CAN YOU OUT RUN A WILD FIRE?

High winds can turn a bush or forrest fire into a WILD FIRE with wind speeds up to 70 mph and temperatures up to 2000 °C, which can and does melt glass and cars.

The fire front speed doubles with every 10º, so speeds for the fire front in a strong wind can reach 140 mph, 210 mph and up to 280 mph.

20o-angle-mathspig-2

What happened to the Smoke Jumpers?

When the fire front changed direction Wag Dodge and 14 other Smoke Jumpers found themselves running for their lives up a steep slope. What did Wag do next?

ANS: Here’s the amazing thing. Wag realised he could not out run the fire at that point. So he stopped. Took off his back pack. Took out some MATCHES and lit a fire in the grassy patch in front of him. Just before the firewall hit he threw himself face down on the burnt patch. He survived. The other 14 firefighters did not.