Archive for the ‘Olympic Maths’ Category

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One Second

June 27, 2016

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Get Ready for the Lego Olympics

February 23, 2012

Get ready mathspigs. You need one Lego Man, Girl, Vampire or Alien each for this exercise. Now we are going to set out the Lego Olympics Athletics track.

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But this story of the Olympics begins with Carl Lewis, one of the greatest athletes of all time who won 9 Olympic Gold medals in 100m, 200m, relay and long jump.

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Carl Lewis

Mathspig needs to find out how big the Lego Olympics track would be. How? Easy.

Carl Lewis will be our standard Lego Man.

I chose Carl Lewis because he kindly gave me his autograph once when I sprinted in high heels across a ballroom floor at a sports dinner in Melbourne and beat all other journalists.  It was my personal best in high heels, I think.

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Lego Olympics to Scale2016……….

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This means everything at the Lego Olympics  will be

1:50

of the real Olympics.

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The  Lego Bird’s Nest Stadium @ Beijing will be 1/50th of the real Bird’s Nest Stadium. (Not the scale shown here). Pictures by Johor Bahru.

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The Lego Beijing Water Cube Swim Centre will be 1/50th of the Real Water Cube.

EXERCISE 1:

Now mathspiggies over to you. The first thing to do is calculate the Lego Olympic measurements (table below). 

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EXERCISE 2:

Then mark out a Lego Olympics 100m sprint to scale and/or

draw a Lego Olympic track (in chalk, perhaps) and/or

step out a Lego Olympic marathon track and/or

make a pole vault pole to scale for your little Lego Man.

Or bring in a Lego Man/Girl/Pirate and step out the Marathon Track (840m to scale).

This little guy has to run 840 m!!!!! Wow!

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Structure

Real

Olympics

Lego

Olympics

100m Sprint

100m

 2m

400m Sprint

400m

42 km marathon

42,000m

Olympic Pool

Length

50m

Olympic Pool

Width

25m

Olympic Rowing Course

2,000m

Equestrian Jump Height

2m

Approx Pole Vault Pole Length

5.5m

Javelin Length

Men

Women

2.6m

2.2m

Olympic Stadium

Straight Segment

Semi-circle Radius inner Lane

Lane Width

84.39m

36.50m

2.5m

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Lego Olympics Flags

February 23, 2012

The Lego Marching band is rehearsing for the Opening ceremony.

Lego Olympics 2016

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………….Bandito (Republic of Baddies)

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Mr Boopy (Bozonia)

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Gorilla Suit Guy (Halloweenotopia)

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………………..Barry the Butcher (Alien Steakistan)

……………..BioHaz (Toxorama)

…………………Dead-Eye Doc (AyeAwArghia)

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Dr Jabb (Bummerville)

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Hula Lula (Grinmania) 

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1. Flag Fractions

EQUIPMENT: Mixed Lego Blocks

Here is the maths. It’s fractions. It’s simple.

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A. National Flag of  Comotosia

They’re a bit sleepy in Comotosia so you better design a flag to wake them up, mathspigs.

The flag must measure ………….   6 blocks x  12 blocks.

One block is a 4 bumps blocks (See pic). An 8 bumps block equals 2 blocks.

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Here’s the catch, mathpiggies.  1/4 of the blocks in the flag must be RED.

How will you do this? (Hint below)

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

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.B. National Flag of Bordom

Once again the Bordonians need a lively flag.

The flag must measure 6 blocks by 12 blocks, but this time it must contain 1/4 red and 1/3 blue. How do you do this?

Hint: Mathspigs! You will have to count the number of red and blue blocks.

 

2. Design A National Flag to Lego Scale

First, name your Lego man, girl or alien and pick a name for their country, planet or crypt.

You will be drawing two flags.

All national flags are rectangles except Switzerland and Tibet, which have square flags but not at the Olympic Games.

Olympic Flags measure:  150 cm x 90 cm

or …………………………….. 60 inches x 35 inches.

These sizes are not equal so which flag is bigger the decimal flag or the Imperial Units flag?

The Imperial units flag is 152.9 cm x 88.9 cm. It turns out the area of the Decimal flag is 13,500 cm2 and the Imperial Flag 13,593 cm2

You will be designing a decimal flag.

Note the Flag ratio of length: width = 150 : 90

…………………………………………………… =  15 : 9 = 5: 3

First design a flag with 5: 3 ratio.  One measuring 10cm x 6 cm would be ideal.

 

BUT

How big are the national flags at the Lego Olympics:

Real flags at the Olympics =  150 x 90 cm

Lego Flag measurements =  150/50 x 90/50 = 3 cm x 1.8 cm = 30mm x 18 mm

Here are my two Lego people with flags  I prepared earlier:

The Enforcer from the Constellation of Obeymia and Mr Boopy from Bozonia.



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Lego Olympic Opening Ceremony

February 23, 2012

The Lego Olympics must begin with a

triumphant Trumpet Fanfare.


Here is the US Army Herald Trumpets playing a rousing fanfare:

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Marching Maths

Three nations are marching one after the other:

Pajamaramas (PJ Boy flag bearer),

The Crytomanians (Mummy’s Boy flag bearer)

and the Berserkers (Olag the Viking flag bearer).

But there is a problem.

They march around the Olympic Track, which is a 400m circuit (inside track).

Lego Olympic Track Circuit = 400/50 = 8 m

But the Pajamaramas, the Cryptomanians and the Beseerkers all walk at different speed. They could just bump into one another and end up in a big heap. So how much time should the officials allow between each country so they don’t collide on the track.

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Speed S1

PJ Boy is a really slow walker

Real life Really Slow walk = 3.0 kph = 3000 m/hr

……………………………………………….= 3000/60 = 50 m/min

Lego really slow walk=   50/50 = 1 m/min

Speed PJ Boy = S1 = 1m/min

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Speed S 2

Mummy’s Boy is a slow walker

Real Life Slow walk = 4.5 kph = 4500 m/hr

………………………………….  = 4500/60 = 75 m/min

Lego slow walk = 75/50 = 1.5 m/min

Speed Mummy’s Boy = S 2  = 1.5 m/min

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Speed S

Olag is a fast walker

Real life fast walk = 6 kph = 6000 m/hr

……………………………… = 6000/60 = 100 m/min

Lego really slow walk = 100/50 = 2 m/min

Speed Olag = S= 2m/min

 

Lego Track Circuit = 8m

Time on circuit (T) in mins:

T = d/S

T = 8.0 /S

The time each nation takes to finish marching around the track will be:

T1 = 8.0/S1  = 8.0/1  = 8 mins

T2 = 8.0/S2 = 8.0/1.5 = 5.3333 = 5 mins 20 secs

T3 = 8.0/S3 = 8.0/2.0 = 4 mins

If you started them all at once there’d be a real pile up.

 

March Time with 1 min gap between groups:

The Enforcer from the Constellation Obeymia will make sure each marching group leaves exactly on time. He will set the clock ticking at 0 mins then enforce a one minute gap between each group.

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Look at the times each nation finishes marching around the track now:

PJ Boy…………………………………………………………………………..

and the Pajamaramas ……………………………………………..8 mins,

Mummy’s Boy and the Crytomanians ………………. 6 mins 20 secs

and Olag and The Beserkers start 2 minutes after PJ Boy and Co and finish at …………………………………. 6 mins.

They will still collide on the track!!!!!

Here are the results for different gap times:

 

 

Nation

March Time

Gap time

0 min

March Time

Gap Time

 1 min

March Time

Gap Time

 2 min

March Time

Gap Time

 3 min

PJ Boy + the Pajamaramas

8

8

8

8

Mummy’s Boy and the Crytomanians

5mins 20 secs

6 mins 20 secs

7mins 20 secs

8 mins 20 secs

Olag and The Beserkers

4

6

8

10

The 3 minute gap works!!!

I think we need a round of applause:

Why not ALGEBRA?

If you had to do this calculation for the entire 205 nations at the 2012 Olympic Games, you can see that your brain might explode.

Da-DA! We can use algebra.

Here is a formulae:

T = d/S + ntg

where

T = time (mins)

from beginning of ceremony.

d= track circuit distance = 8 m

S = speed m/min

n = nation march order number = 0,1,2,3,etc

tg = time gap between nations (mins) = 1, 2, 3, 4 etc    

TRY IT, mathspigs!!!!!

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Lego Olympics Triathlon

February 23, 2012

This is the Lego Triathlon.

And, mathspiggies, your Lego Man/girl/alien has made it into the finals. 

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EQUIPMENT: Your Lego Man, girl, alien, your brain, a calculator & one dice.

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In the Olympic Triathlon contestants:

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Swim 1.5 km = 1,500 m

Cycle 40 km = 40,000 m

Run 10 km = 10, 000 m

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In a Lego Olympic Triathlon little Lego men, girls, aliens have to:

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Swim 1,500/50 = 30m

Cycle 40,000/50 = 800m

Run  10,000/50 = 200m

But each contestant will be better at some section than another.

Your Lego man, girl, alien replaces one of the following contestants. Transfer their number and times to your column.


Now calculate the Total Times for each contestant.

THEN roll the dice.

3. Disqualified because your coach gave you an alien Smoosnot drink with banned drugs by mistake.

5. Disqualified because a Groppanator from the Urgastor Galaxy ran out of the crowd just before the finish line and hugged you with his 6 arms.

Triathlete

30 m Swim

Speed

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Time

800m Cycle

Speed

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Time

200m run

Speed

+

Time

Total

Time

mins

Roll

3 or 5

Disqualified

1

Mummy’s Boy from Crytomania

40 m/hr

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400 m/hr

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250m/hr

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2

PJ Boy

from Pajamarama

30 m/hr

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200 m/hr

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500 m/hr

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3

Olag

from

Beserk

40 m/hr

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200 m/hr

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500 m/hr

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4

Dead-Eye Doc

from

AyeAwArghia

60 m/hr

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400 m/hr

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450 m/hr

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5

Hula Lula from

Grinmania

50 m/hr

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400 m/hr

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500 m/hr

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6

Mr Boopy from

Bozonia

30 m/hr

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600 m/hr

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200 m/hr

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7

Gorilla Suit Guy

from

Halloweenotopia

50 m/hr

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500 m/hr

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300 m/hr

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8

BioHaz from

Toxorama

60 m/hr

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500 m/hr

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400 m/hr

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from

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Who won?

You can work it out mathspigs.

Total Times are published @ the end of The Lego Olympics Closing Ceremony.

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Lego Olympics Closing Ceremony

February 23, 2012

The closing ceremony is chaos. All the athletes crowd together.

There is one last lot of calculations, mathspigs.

Think about this.

% Gold Medal Winners:

At the 2012 London Olympics there were 47 Gold medals awarded in athletics.

There will be 2,000 athletes competing for these medals. Now some athletes will win more than one Gold medal and some events eg. the relay race involve more than one athlete. Each member of the winning relay team wins a Gold Medal.

Approximately what % of athletes won’t win a Gold Medal at the London Olympics?

Ans:  97.65%

Probability of Winning a Gold Medal:

Ha-HA! Tricked ya! Such a calculation would be meaningless.

The core to all probability is, or should be, RANDOM SELECTION.

Lottery balls fall randomly into the tube. But the Olympic athletes represent a BIASED SAMPLE. Athletes are selected for the games. They must qualify for an event. They train. The chance of one athlete winning is quite different from that of another.

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Eight numbered  100m-sprint athletes is a Biased Sample.

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Eight numbered lottery balls in last nights draw make up a random sample.

This brings us to the end of the Lego Olympics.Lego Olympics 2016

We will finish with  some Lego fireworks.

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Lego Olympics Triathlon total Times: 1. Mummy’s Boy: 3 hrs 33 mins, 2. PJ Boy 5 hrs 24 mins, 3. Olag 2 hrs 51 mins, 4. Dead-Eye Doc 2hrs 57 mins, 5. Hula Lula 3 hrs, 6. Mr Boopy 3 hrs 20 min, 7. Gorilla Suit Guy 2hrs 52 mins,8. BioHaz  2 hrs 36 mins.

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How fast are Our Olympic Athletes?

September 30, 2011

First we have to calculate the speed or velocity of an athlete.

Event distances are recorded in m (The Olympic Games uses the Metric system) and time in minutes, seconds and 1/100ths of a second except cycling where 1/1000ths of a second are recorded.

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Here is Usain Bolt creating a New World Record for 100m in Berlin 2009. You may as well watch. It will take less than 10 secs.


We are going to use current Olympic Records to calculate the average speed of Usain Bolt, the fastest man on earth:

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But we are more familiar with km per hr (kph) so we will convert from m/sec to kph:

Some in the world use mile per hr (mph) so one more conversion:

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Maths Exercise:

Here are some current Olympic Records, which students can use to calculate average speeds in m/sec then convert these speeds to kph (See chart in the following post for answers);

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1. 100m M Sprint 9.69 sec Usain Bolt Jamaica

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2. 100m W Sprint  10.62 sec Florence Giffith-Joyner  USA

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3.  100m M Freestyle    47.05 sec   Eamon Sullivan Australia

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4. 100m W Freestyle  53.12 sec   Britta Steffen Germany

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5. 1500m  M Freestyle   14.38.92 mins Grant Hackett Australia

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6. 200m  M Butterfly   1.52.03 mins   Michael Phelps   USA

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7. 200m  W Butterfly    2.04.18  mins    Lui Zige  China

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8. 1,500m M Track   3.32.07  mins     Noah Ngeny  Kenya

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9. 1,500m W Track  3.53.96 mins   Paula Ivan  Romania

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10. Marathon 42.195 km   M    2.06.32 hrs   Samuel Wanjiru    Kenya

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11. Marathon  42.195 km  W  2.23.14 hrs    Naoko  Takahashi   Japan

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12. Cycling M 200m Sprint   9.815 secs   Chris Hoy  UK

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13. Cycling  W 200m Sprint  10.963 secs  Victoria Pendleton UK

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14. Rowing M 8+   2000m  5.19.85 mins   USA

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15. Rowing  W 8+  2000m   5.55.50 mins   USA

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16. Cycling M 1km Time Trial  1.00.711 mins  Chris Hoy   UK

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17. Cycling W 500m Time Trail 33.952 secs Anna Meares Australia

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You will find more Olympic records at these links: track, cycling and swimming:

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How fast are Olymic athletes compared with animals?

The top speed of humans was clocked at 43.56 km/h (27.1 mph) by Olympic sprinters Michael Johnson and Donovan Bailey during their Olympic competitions. This top speed only lasts for very short bursts. More info at this link.

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I’m sure Usain Bolt would achieve an even higher burst of speed if being chased by a cheetah. And, of course, cyclists can go much, much faster down hill.

So lets see how our 15 athletes above would rank on the animal speed chart. Go to the next post. Woo HOo! It’s the Zebra Olympics.