Archive for the ‘units length’ Category

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7. You can safely jump from a burning skyscraper/bridge/aircraft into water.

December 13, 2018

Angels and Demons (2009) Tom Hanks character, Robert Langdon, hero of Dan Brown’s jumps from a helicopter and falls thousands of feet into Rome’s Tiber River and survives, of course.

Ahhhh! Look up. It’s raining Tom Hanks!!!!!The Hulk (2003) The Hulk hops from the Golden Gate bridge onto a jet fighter, whose pilot tries to get rid of him at high altitude. The Hulk falls off and plummets many thousands of feet into the bay. He survives.

There are 2 factors we must consider when jumping or diving from a great height:

1. Surface Impact

2.Water depth 

1. Surface Impact

According to the Free Fall website falling into water is not a good survival strategy. 

‘Someone falling without a parachute from more than 2,000 feet or so would be falling quite a bit faster than 100 miles per hour (161 kph) The folks who have survived falls into water have had streaming parachutes above them, which probably slowed their falls to the 60 mph range (97 kph). Having a streaming parachute helps in another way because it aligns the body in a position where the feet enter the water first.’

The website goes on to explain that water is an INCOMPRESSIBLE FLUID. It’s like landing on concrete. Landing in mud, on snow, on trees, on circus tents etc helps break the fall. Moreover, jumping off a bridge into turbulent sea may be safer than jumping into calm water.

On 24th Oct 1930, Vincent Kelly, 31, while working on the Sydney Harbour Bridge fell 170 ft (52 m) into Sydney Harbour and survived.

A champion diver he did several summersaults and landed feet first. He broke a couple of ribs as he did not enter the water at a perfect RIGHT ANGLE but rather a few degrees off perpendicular..

2. Water Depth

The next issue is, if you are going to dive or jump into water from a great height and, miraculously, survive the impact, how deep should the water  be?

Olympic divers often practice their dives in a bubble pools (like a spa). This reduces the impact for a bad dive but the water must be much deeper. Sports Smart Canada recommends a water depth of double the height of the drop. But is this realistic if, say, you are jumping or diving from the top of a waterfall into aerated water.

You can work out approximate depths needed if you were jumping into calm water from heights such as below:

How deep do you plunge? The answer is surprising because, in fact, you decelerate really fast in water.

See REd Bull Jump Science here

Thanks to Rod Vance  for the Fluid Engineering Calcs (done by hand … not by computer program) for calculating the depth of water when your feet stop moving. That is the minimum depth of water needed for the jump (See graph below)

NOTE: Even with this fancy maths assumptions must be made about the transition epoch-half in/half out of the water.

 Assuming you survive the impact and you breath out through your nose – to stop water going up your nostrils really fast- then you will not go any deeper than approx 4 m or 13 ft from a platform of 20 m (65 ft) or less.

If you’re diving into water from, say, a helicopter as in the Demons & Angels movie you don’t need extremely deep water. Assume Langdon was at 100m (328 ft) or the height of The Statue of Liberty(above) or a 33 story building  when he jumped, then extrapolating the graph (above), maybe, a depth of 5m (16 ft) would do.

If you want to see what looking down from a 58.8 m (193 ft) platform looks like check out thisWorld Record Jump by Laso Schaller.

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Winter Olympics: Beaten by 0.001 seconds

February 14, 2018

 

In 2014 Winter Olympics Annette Gerristen (below) lost the Gold Medal in the 1000 m Women’s speed skate competition by 0.02 seconds.

Annette Gerritsen fromthe Netherlands

Annette Gerritsen fromthe Netherlands

What are the speed skating times for women?

Women’s Speed Skating Calulations:

Here are the speed calcs for Yara Van Kerkhof of the Netherlands in the 2018 Winter Olympics:

If Yara lost the Gold Medal by 0.02 secs (2 hundredths of a second) what would the distance be between the Gold and Silver place getters?

When 1st and 2nd place are separated by 0.02 seconds, they are travelling at almost the same speed. So the second place contestant is:

23.8 cm behind the Gold Medalist

The 2018 Olympic Gold Medalist in the 500m Women’s Speed Skating was Arianna Fontana.

Italy’s Arianna Fontana wins the 500 m Speed Skating 2018 Olympic Gold Medal in 42.569 seconds ahead of Yara van Kerkhof of the Netherlands and Kim Boutin of Canada. 

Men’s Speed Skating:

At longer distances the men’s speed skating speed is similar to the women’s speed above.

If you lose by  0.001 secs…………

Apollo Ono (below) competed in the 1500m men’s speed skating. He has won 8 Olympic Medals.

If a speed skater lost the Gold Medal by 0.001 seconds, the smallest measured time segment at the Olympics, they would be:

1.19 cm

behind the winner. That is less than the length of a small fingernail.

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Hello 2018 This is why you need maths!

December 30, 2017

Hello Little Munchins,

,…………………………………………..…………………………….

Maths can save your life. How? Read on.

,…………………………………………..…………………………….

Sadly, a car has been used as a weapon again in my city, Melbourne. 

,…………………………………………..…………………………….

When talking to science types about the Maths of a Car Used as a Weapon they say ‘Yeah! Right! As if you are going to stand around doing the maths when a car is heading towards you!!!!.’……………………

NO!…………………………………………..……..

You don’t do the maths in a crisis. You do it before hand. And it will change your view of car safety for all time.

METRIC:

Maths of a Car Used as a Weapon 

If you are 9 m away from a car travelling at 60 kph, you DO NOT have time to move out of the way. 

Some survival tips at the above link.

USA UNITS:

Maths of a Car Used as a Weapon

If you are  28  ft away from a car travelling at 35 mph you do not have time to move out of the way.

Some survival tips at the above link.

Stay safe in 2018.

Cheers

Mathspig

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1a. The WORLD POPULATION as ONE BIG CROWD … METRIC

December 9, 2017

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1b. The WORLD POPULATION as ONE BIG CROWD … USA Units

December 8, 2017

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8c. What Volume of Alcohol is Lethal?

August 14, 2017

The Complaint

8c: I Will Never Use this Maths

The Solution:

You are going to use this maths NOW……………..

……………………………………………………………………..

How much alcohol will kill you?

TOPICS: Decimals, %, algebra, vol, weight units (Metric)

At low levels of consumption alcohol impairs decision making and inhibits coordination. It makes you DUMB and CLUMSY, which can cause serious injuries if you, say, fall down stairs.

Legal Age to Buy or Sell Alcohol USA: 21 years

Legal Age to Buy or sell Alcohol AUST, NZ & UK: 18 Years

Legal Age to Buy or sell Alcohol CANADA: 18 – 19 Years depending on region.

At higher levels of consumption ALCOHOL can kill. It is a depressant. It acts on your central nervous system. It can STOP YOU BREATHING.

WORKSHEET PDF:  How Much Alcohol Would Kill You? WORKSHEET

WORKED EXAMPLE

1. Calculate the weight of (pure) alcohol or ethanol in the following standard drinks using the following information:

Now Ethanol =  0.79 gm/ml

More information @ alcohol.org.nz

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9. I Hate Answering Questions in Class: BUSTED

August 10, 2017

The Complaint:

 

9. I Hate Answering Questions in Front of the Class

 

The Cause:

Students worry about getting the answer wrong in front of the class because they believe that maths answers are always either RIGHT or WRONG.

The Solution:

The maths we need in the REAL world often involves open ended questions. Think of finding directions on Google Maps. What is the best way to get from A to B? One route might be shorter but include tollways another might involve longer distances but less traffic. 

Text book problems are often repetitive with RIGHT answers at the back of the book. But in the real world maths problems nearly always involve THINKING. eg. A building design might require specific engineering maths. Now add costing! That’s an open question. There are many options. Maybe the costing will then change the engineering. Build 20 stories instead of 25.

Thinking Outside the box in Education: Info and Toolbox: here

Prof Peter Liljedahl, Faculty of Edu, Simon Fraser Uni, Canada, advocates  open ended questions in the maths classroom.

Here are some of his examples for Year 7 -9 (Download pdf file at the link):

Concert in Toronto;

You have won tickets to a concert in Toronto but must plan your trip using flight times to arrive at the concert by 9pm.

Two Bike Race:

You are in a bike race and have to use a street bike and trail bike, but one bike must be left somewhere on the route.  You travel at different speeds depending on which bike you use. What route do you take? (A basic map is included.)

Something inspiring:

Maths is often about playing around with answers. This is how play led a class of 12 year olds to produce a peer reviewed research paper published in a science journal.