Archive for the ‘Rates’ Category

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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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One Second

June 27, 2016

1 Second Logo

1 Second Logo 2a

1 second 1 Mathspig1 Seccond 2 Mathspig1 Second 3 Mathspig

1 Second 4 Mathspg

1 Second 5 Mathspig1 Second 6 Mathspig1 Second 7 Mathspig1 Second 8 Mathspig

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Hair Maths 3: How OLD is your hair?

April 30, 2015

1 Mathspig 1980s hair

2 Hair follicle

The follicle diagram (above) came from bgoffforensics blog. More on hair growth rates here.

QUESTION 1:

3 Mathspig how old is your hair!!!!

4 Mathspig 1970s celebrity hair

QUESTION 2: 5 MAthspig world's Longest Dreads

The growth rates of 1.25 cm/month or 0.5 inches/month are rounded off. Calculations using these growth rates will produce different answers for very large numbers (as above). Read more about the above story in the Daily Mail, UK here. By the way, Asha has been growing her hair for 25 years. Her hair weighs 3 stone or 19 kg. You can find more hair records including the World’s longest ear hair here.

QUESTION 3:

6 Mathspig Natasha's hair

Natasha lives in Rio de Janeiro, Brazil. Read more about Natasha in the Daily Mail here. Once again Mathspig has rounded off the length of hair for easy calculation. The Daily Mail puts Natasha’s ‘mane’ at 5 feet 2 inches or 157 cm. This is the length of hair to be cut off. So Mathspig adjusted the length to 180cm or the approx length of her longest hair.

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MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig …………………………………………………. with Kerry Cue

April 25, 2015

Mathspig Maths Mystery Box

Helloooo My Little Luvvies,

 

So here are the 10 Maths Mystery Box challenges I’ve put together for you:

1. Maths Mystery Box 1: NOT STUPID

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2. Maths Mystery Box 2: CURIOUS

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3. Maths Mystery Box 3: NERD

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4. Maths Mystery Box 4: FUNNY THAT

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5. Maths Mystery Box 5: FANTASY

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6. Maths Mystery Box 6: WEIRD

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7. Maths Mystery Box 7: PHONES

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8. Maths Mystery Box 8: JUNK FOOD

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9. Maths Mystery Box 9: MUSIC

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10. Maths Mystery Box 10: LETHAL

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mathspig bonusAnd the bonus Maths Mystery Box Question:

Sniffer rats have been in the news this week, but:

 When is a sniffer rat better than a sniffer dog?

(Hint: It has to do with a measurement?)

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Isn’t MATHS marvelous? And magical too!

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Hoo Roo for now,

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MATHSPIG

 
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Maths Mystery Box 9: MUSIC

February 13, 2015

Maths Mystery BOX 9

Middle School Maths Challenge

Rates, averages and crazy drummers (That’s all of them, man!)

Here are 3 classic rock songs. Listen to the tracks and find the beat per minute or bpm of each song. 

HINT: Count the beats and ask a friend to time you.

Beat 1: AC/DC …  T.N.T.

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Beat 2: Queen …  Another one bites the dust

bpm for above clips here

 

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Beat 3: Uptown Funk …  Mark Ronson

Lyrics may offend some.

Find the Uptown Funk bpm here.

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BIG challenge 1:

Ramon

Drummer: Ramon Sampson

Pick one beat and see if you match the exact bpm. If you don’t have drumsticks use pencils.

HINT: Count the beats and ask a friend to time you.

BIG challenge 2:

Record yourself drumming to your own natural beat for 10 seconds.

Listen to your recording and count the beats. Multiply by 6 and you have your bpm.

Do this 4 times.

Calculate your average bpm.

Then for each of the 4 trials calculate the % error.

bpm % error

Pro drummers do not like to be out by 1 beat or 1 bpm. They want to hit ZERO % error. I beat out per minute for a bpm = 84 would mean an error of approx 1%. 

Learn about the strangeness of drummers brains here.

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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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MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig …………………………………………………. with Kerry Cue

January 2, 2015

Mathspig New Year Res 2015

Hellooooooooo Sweeties,

This has to be the best way to save the planet. Yes! Eat up my little lovelies. For every kilo you pack on, you reduce your carbon footprint. Isn’t that the best news for piggies everywhere!!!!! You will find the yummy maths here:

How to pig out and save the planet

Meanwhile, here are some other mathsy things to do with pigging out for fun and profit:

Who uses more calories to travel 10 km: mini or man?

How far do you have to walk to walk off 1 kg of fat?

How far can a biodiesel car drive on 1 kg of human fat?

  ………………………………………………………………………..

Cheerio my Chubbies

Mathspig