Posts Tagged ‘Middle school’

h1

Winter Olympics: Bad Math of Figure Skating Scores

February 22, 2018

According to the fab NBC video, Mathletes,  nine Figure Skating judges score competitors for the complexity of each element (eg. Triple axel or triple spin jump) and the quality of the performance producing a score out of ten.

Tessa Virtue and Scott Moir win GOLD at Pyeong Chang 2018

                                   Kailani Craine, Australia

figure skating score 9 judges nbclearn

This is a typical figure skating score card for one competitor.

The final score, however, is based  on the average for only 5 of these scores. Two are eliminated by random selection (Red Brackets). Then the top and bottom scores are removed and the remaining five scores averaged.

Screen grab NBC Mathletes

Screen grab NBC Mathletes

……………………………………………………

Now consider the IDENTICAL SCORE CARDS

of Skater A & B:

figure skating score A

Skater A:

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them)

7.00 + 7.00 + 7.00 + 6.75 + 7.00

……………………………………..

=  34.75/ 5 = 6.95

figure skating score B

Skater B:

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them). But this time the random selector eliminates two low scores.

The average:

7.00 + 7.25 + 7.00 + 7.00 + 7.00

……………………………………..

=  35.25/ 5 = 7.05

Same score cards but Skater B gets a higher average score than Skater A.

Skater A is, in fact, beaten by a random number selector!!!!

Advertisements
h1

WINTER OLYMPICS: How ski Jumpers Use Math to Increase their Jump Length

February 16, 2018

While air resistance has little impact on aerial skiers it is a significant factor used by ski jumpers to increase their jump distance.

The significant maths for ski jumpers is therefore X-section area.

Here is the jump at Pyeong Chang, 2018. Just imagine going down that at top speed!!!

              A ski jumper is set to jump in Pyeongchang.

                   Casey Larson USA Pyeong chang 2018

Ski jumpers increase their speed going down the ramp by reducing their X-section area:

Lindsey Van, USA, practicing in a wind tunnel

           Lindsey Van, USA, practicing in a wind tunnel

Once they leave the ramp, ski jumpers try to increase their X-section area like Ski Divers to slow their vertical fall. But they have to land safely so they keep their skis at a minimum  angle.

Abby Hughes, USA, practicing in a wind tunnel.

Abby Hughes, USA, practicing in a wind tunnel.

Abby Hughes, USA, in the air

          Abby Hughes, USA, in the air

Here are the X-section areas for Abby Hughes*:

Abby Hughes X-section

Here is the formula for Air Resistance of Drag:

D = ½CApv2

Where C is the drag coefficient or constant, which depends on the shape and spin of an object. It is found by testing the object in a wind tunnel.

A is the X-section Area,

p is the density of the air and

v the velocity of the object.

More here.

As Abby Hughes has tripled here X-section area in the air she will have tripled the vertical drag during her jump. This will slow here decent.

*Mathspig calculated the X-section area by the old fashioned method of counting squares and rounding off the final count. Mathspig sized the two pics of Abby Huges so that her head was the same size in both pictures.

h1

WINTER OLYMPICS: One Rule Aerial Skiers Cannot Break

February 10, 2018

Aerial skiers aim for height rather than length. Their aerial flight times are much smaller than ski jumpers so air resistance has minimal impact.

In fact, there is one law the aerial skiers cannot break. It is the law of gravity.

Here is an equation for  projectile motion from Wired magazine.

Screen grab from Wired Magazine

Screen grab from Wired Magazine

The equation for projectile motion also applies to Motorbike Jumps and Longbow Arrows.

Here is the x-y graph for different launch angles.

trajectory wired magazine

trajectory wired magazine

 

You can go to this page for complete calculations. Aerial skiers twist and turn but their CENTRE OF GRAVITY must follow this graph. More on centre of Gravity at The Great Back Pack Attack ie.

The centre of gravity of Aerial Skiers must follow a

parabolic curve.

Aerial Parabola final 2

Rocky Maloney Winter X Games Aspen

Rocky Maloney Winter X Games Aspen

h1

10 Reasons Why Students HATE Maths: BUSTED

December 17, 2017


1. Maths is BORING!: BUSTED

 

2. I’ve got a BAD maths Teacher: BUSTED…………………………………………………………………………….

 3.  Everyone Hates Maths Anyway: BUSTED

…………………………………………………………..

4. Too many different ways to do the………..

same thing: BUSTED

………………………………………………………………………………

5. It’s Too Hard: BUSTED

Come one, a racoon can do it!

 

 

6. You’re either Good at Maths……………………….

or You’re Not: BUSTED

………………………………………………………………….

7. Maths is really SCARY!: BUSTED

………………………………………………………………………….

8. I’ll NEVER use this MATHS: BUSTED

………………………………………………………………..

9. I Hate Answering Questions in…………………

Class: BUSTED……………………………

………………………………………………………………

10. They’re Always Giving Us New Stuff: BUSTED

 

h1

1. Maths is BORING!

December 9, 2017

Middle School Maths that is AMAZING

psst! That means it’s not boooorrrrinng!

NEW POSTS!

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

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

2a. If all the cars in the world were parked together what area would they cover? Metric Units

2b. If all the cars in the world were parked together what area would they cover? USA UNITS

3. If you put the population of the world into AUSTRALIA what area in m2 would we get each?

Meanwhile this Mathspig blog is full of AMAZING middle school maths such as:

KARATE MATHS

HOW MUCH BLOOD CAN YOU LOSE AND SURVIVE?

WHAT VOL OF ALCOHOL IS LETHAL FOR TEENS?

THE TERRIFYING MATH OF RUNNING FROM A BEAR USA UNITS

THE TERRIFYING MATHS OF RUNNING FROM A BEAR METRIC UNITS

PARABOLAS AND THE ART OF SPIITING WATERMELON PIPS

h1

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

December 9, 2017

h1

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

December 8, 2017