Archive for the ‘Sport Maths’ Category

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FOOTBALL MATHS: THE LONGEST KICK

June 3, 2016

Mathspig Football Maths 1

Mathspig football Maths 1a

Mathspig Football Maths 2aMathspig Football Maths 3Mathspig Football Maths 4

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The following maths is suitable for Year 9+

but can be presented to lower grades just to show

maths is cool!

Mathspig Football Maths 5Mathspig Football Maths 6bMathspig Football Maths 7

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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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5. Beaten by 0.001 seconds

January 23, 2014

Here is a screen grab from the  New York Times article on Speed Skating:

Fractions of a Second: New York Times

Fractions of a Second: New York Times

Annette Gerritsen fromthe Netherlands

Annette Gerritsen fromthe Netherlands

Annette Gerristen lost the Gold Medal in the 1000 m Women’s speed skate competition by 0.02 seconds.

Apollo Ono USA speed skater

Apollo Ono USA speed skater

Screen Grab NBC Mathletes Apollo Ono Recorded Speed

Screen Grab NBC Mathletes
Apollo Ono Recorded Speed

From the wonderful NBC Mathletes Video

How far can a speed skater travel in 0.02 secs?

speed skate maths

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 winner.

The distance travelled by the winning speed skater in 0.002 seconds would be:

2.38 cm.

So the second place competitor would be 2.38 cm behind.

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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Trick 10: Math Mentalist Devises Foolproof Gambling System

November 30, 2012


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Math Mentalist Devises Foolproof Gambling System

Requirements: Smart board/Data Projector

or Chalk & Talk

This is the most awesome way to introduce probability.

Mentalist Derren Brown devises a foolproof gambling system. He sends a girl , Kadisha, the number of a winning horse in race to be run the next day. It wins. He sends her the winning horse and race number 4 more times. She ends up with winnings close to £ 1000 before the final race. Derren convinces her to borrow money for the last bet. She does. She places £4,000 on a horse. Did it win?????

Watch Part 5 of The System

 

 

If you are not convinced Derren Brown can come up with a foolproof system for horse race tipping, let me explain The System. He took 7,776 e-mail addresses, divided them into 6 equal groups and sent each group a different number for a horse in a 6 horse race to be run the next day. Naturally, one group of 1296 had been given the winning horse number.  This group was divided into 6 again and given the number of the ‘winning’ in a six horse race the next day and so on.

Race 1: 7776

Race 2: 1296

Race 3: 216

Race 4: 36

Race 5: 6

Out of 7776 punters, only one punter was given in advance five horse race winners in a row. Was it Kadisha. You will have to watch the Youtube above.

You can watch THE SYSTEM in full here. It takes 47 mins.

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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!!!!!