Australian Open 2020: Could YOU ….. return Roger Federer’s serve?

The Australian Tennis Open is being played at the moment and Mathspig is always amazed at the serve speed of the top-seeded players.

Here are some of the serves speeds of players in this year’s Men’s Open. 

Keep in mind the fastest female tennis serve by Barbora Záhlavová-Strýcová is a very respectable 225 km/h (140 mph).

Can you return Roger Federer’s serve?

NOTE: Andy Murray had the same serve speed as Roger Federer.

Go here to see why this simplified calculation works! 

Mathspig tested her reaction time here. TRY IT!

Mathspig’s best, best, best reaction time = O.33 sec

Could Mathspig return Roger Federer’s serve?

Nooooo!…………………………………………………………………….

I’d be hit in the head by a speeding tennis ball

before I even moved.

But I’m a pig. I’ve got the best service GRUNT! Ha!

Amazing and Terrifying Wildfire Maths . . . . . . . . . . . . . . METRIC UNITS

 

With the catastrophic Californian fires burning into November and wildfires currently burning in NSW and Qld, Australia, I had to repost this firefighter maths for middle school classrooms.

Radiant Heat Stats WA Fire Dept FACEBOOK, Australian Bushfires 14 NOV 2019 MyFireWatch WA

 Wildfires USA 2019 Map: Ecowest,

METRIC UNITS

Background Story

On 5^th 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:

t_av = (t₁ + t₂ + t₃₎/ 3 =

Your Speed S = 10/t_av = ……… m/sec

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

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.

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.

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.

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.

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.

Why do so many students HATE MATH? … um, you know, BOREDOM

According to ‘Bored Out of Their Minds’, an article by ZACHARY JASON in The Harvard Ed Magazine (2017):

Boredom accounts for nearly a third of the variation in student achievement. 

Half of high school dropouts cite boredom as their primary motivator for leaving.

Boredom begins for Math students at Grade 6 when students (Common Core Standards, USA) tackle more abstract concepts such as linear eqns, exponents, probability, geometry and so on.

Math curriculums in the USA, UK & Australia all demand students solve REAL LIFE problems. Too often these are of the type:

Q. Ronaldo has tethered his goat on a 12ft rein in the corner of a 20ft square field. What area can the goat graze?

THE ANS: Who cares?

Simple.

Ask students maths questions which have answers they want to know.

Students really don’t care about Ronaldo’s goat, but here are some questions which involve intriguing answers they might want to work out. And many of these questions involve funny or age-relevant activities, which also helps engagement.

1. Mean, Median STATS: Mean, Median and Coffee: Busting an Urban Myth

2. Parabolas: Can you beat the 12-14 yo World Record for a Watermelon Pip spit?

3. Geometry: Build a Freestanding Tower

Rates (Speed) & Units:

4a. The Terrifying Math of Running from a bear

USA Units

METRIC UNITS

4b. How old is your hair?

5. Decimals, %, Volume: What Volume of alcohol is lethal for teens?

6. Decimals, Algebra, Weight Units

How much blood can a kid lose and survive?

USA UNITS

Metric Units

Graph Hunger Game Math

7. GEOMETRY. Angles

Why killer heels can kill!

Any Topic:

8. Middle School Math Photo Scavenger Hunt

9. Write Your Own Math Song

Space Math Song here

10. Make a Math Poster

EVEN TEACHERS GET BORED!!!

The average time it takes an audience at a conference to switch off is 11 minutes. Keep in mind this audience is, at least, being paid to be bored witless.

1. You can duck a bullet

You will find all the ballistics stats you need here:

2.You can out run a fireball?

In nearly every Action Movie our hero possibly holding hands with his love interest will run and jump ( just in time ) out of the way of explosion. eg. Man on Fire (2004) with Denzel Washington, The Marine (2006) with John Triton, Mad MAX FURY ROAD (2015) with Charlize Theron and Predator 2 (1990) with Danny Glover .

We will use car bomb stats that come from the U.S. Bureau of Alcohol, Tobacco and Firearms. (We in Australia can only assume this bureau exists because, um , there are many exploding cigars in America.) You will find these at Car Bomb Response.

 

3. You can out run machine gun fire

Mathspig is amazed. She didn’t think there would be any hope of survival. But if the baddies sweep the machine gun tracking you as you run then …. see calcs below.

Are you feeling lucky Punk?

5. You can jump out of an airplane that is about to crash and catch the baddie who took the last parachute.

 The names Bond, James Bond. In Moonraker  with Roger Moore (1979) 007 jumps out of a plane without a parachute to avoid an assassination attempt. He catches up with, Jaws, arch-baddie, in mid-air and takes his parachute. Jaws survives his fall by landing on a big top circus tent.

In Point Break with FBI agent Johnny Utah, Keanu Reeves, leaps from a skydiving plane after Patrick Swayzes’ characer, Bohdi, who has taken the last parachute. Utah catches Bohdi in mid-air, and after a tense confrontation with a gun, both survive using Bodhi’s chute. The remake was in 2015.

There are more movie and real life stories at the  Free Fall Maths link.

Note: We’ll assume Bhodi and Utah have equal horizontal velocities (plane exit velocity plus wind) so the following calculations only involve the vertical or falling velocity. The terminal velocities used for Bhodi and Utah are realistic estimates. 

6. If the pilot dies the control tower can talk you down.

So mathpigs, here is a small taste of what you would need to do to land a small aircraft in an emergency if the pilot is unconscious/dead.

A = Airspeed

Find airspeed indicator on instrument panel.

Instrument Panel Piper PA-28

Check speed.

Knots or mph or kph?

Avoid red zone. Too fast.

Knots outer scale. mph inner scale. Recommended velocity between blue & red.

B = Contact nearest air traffic controllers. 

1. Call MayDay MayDay MayDay

2.  Look for plane ID. It will be on instrument panel somewhere.

3. Check fuel.

On the Piper Cherokee there are 2 fuel tanks, R & L. Check both.

Check aircraft operating handbook to see fuel consumption and remaining time in air.

Quick calc.

 

C = Checklist

Follow Emergency Landing Checklist in aircraft operating handbook for Power OFF or Power ON landing.

Keep in mind, if your air speed is too low you can drop from air, but the higher the landing speed the bigger crash.

Crash energy increases with the square of speed. It’s a parabola!!!!!

The likelihood of a passenger with

NO flying experience landing a plane safely in an emergency is

very small.

The likelihood of a passenger with

NO MATHS skills landing a plane safely in an emergency is

ZERO.

 

8. You can survive any amount of beating in a fight.

 

 

 

 

Every action hero gets into a fistfight. James Bond, Jason Bourne, Indiana Jones. Then there are all the stars known for their fight scenes. Sylvester Stallone ( Rocky),  Arnold Schwarzenegger (True Lies), Jackie Chan (Any movie), Bruce Willis (Die Hard 1,2, 3 etc), Mel Gibson (Lethal Weapon I, II, III etc), Jean Claude Van Damm (Blood Sport, Street Fighter), Brad Pitt (Fight Club), Fast & Furious 1,2,3 and so on.

But can the human body take this punishment?

We can work it out. Measurements taken at The University of Manchester have shown that local boxing hero Ricky ‘The Hitman’ Hatton really does live up to his name. (DailyScience)

Ricky ‘The Hitman’ Hatton can pack a punch!!!!! 

Similar results were found at Uni Manchester BBC (Force of boxer’s punch measured)

So one punch is equal to being hit by a car …… if only for a split second!!!!!!!!!!! Nevertheless you can be killed by this one punch.

You’ll find some great punching physics here

9. A single match or candle will light a room the size of a football stadium.

 

This is the rework of a previous post.

Action heroes such as Indiana Jones or even film kids like Tom Sawyer or The Goonies who go into a cave, anabandoned house, a crypt or a catacomb light the entire place with one match, one candle, a lighter or a cellphone.

Is this real?

 

Now mathspigs, if you are interested in a career in stage/film lighting or even architecture you will need this maths.

 

60Watt light globe tells us how much power it uses. But some 60W globes are brighter than others. Light is measured with weird units.

USA uses Foot-candles. Can you imagine the pickup line ‘You brighten up my world like a footcandle’? A foot-candle is the brightness of a candle 1 foot away. Now think of a bubble around the candle. Brightness is mostly measured using one square foot or one square metre of that bubble:

1 LUMEN = 1 Footcandle/ft squared

1 LUX = 1 footcandle/m squared

Don’t get too hassled by these units.  As a rough rule:

1 candle = 1 LUX

From graph you can see by 3m a Birthday Cake is not very bright even in a haunted house or crypt.

Challenge: Draw a graph of the brightness of your own Birthday Cake!

Big Challenge:Draw a graph of your Teacher’s Birthday Cake!!!!!! Ahhhh!!!!

We know:

1 candle = 1 LUX

Now compare the brightness of 1 candle to the brightness of other sources of light:

If you want sufficient light to live your everyday life you’d need:

80 candles just to go to the toilet!!!!!!