Posts Tagged ‘speed’

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

January 27, 2020

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!

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

November 13, 2019

mathspig-smoke-jumpers 

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,

mathspig-metric-units-fire-math

METRIC UNITS

Background Story

On 5th 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:

tav = (t1 + t2 + t3)/ 3 =

Your Speed S = 10/tav = ……… m/sec

mathspig-firefirghter-maths-1

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

mathspig-firefighter-maths-2

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.

mathspig-fire-fighter-table-1

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.

mathspig-cfa-diag

mathspig-fire-fighter-table-2

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.

mathspig-fire-fighter-table-3

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.

20o-angle-mathspig-2

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.

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Amazing and Terrifying Wildfire Maths . . . . . . . . . . . . . . USA UNITS

November 13, 2019

mathspig-smoke-jumpers 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,

mathspig-usa-units-fire-math

 

USA UNITS

Background Story

On 5th 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?

USA UNITS

Time Trial:

Mark out a 30ft course. Make 3 time trials.

t1 =

t2 =

t3=

Average your time:

tav = (t1 + t2 + t3)/ 3 =

Your Speed S = 30/tav   ft/sec

mathspig-firefirghter-maths-1

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 12mph (up to 20mph) in a gentle breeze.

Fire Front Speed Grass Fire

Fire Front Speed = 12 mph = 12 x 5280/(60 x 60)

                           = 17.6 ft/sec

                           = 18 ft/sec

mathspig-firefighter-maths-2

CAN YOU OUT RUN A FIRE?

Average Running Speed Boy 13–14 yo = 10 ft/sec

Average Running Speed Girl 13–14 yo = 8 ft/sec

We’ll assume, boy or girl, that you are really motivated and can run away from the fire at top speed of 10 ft/sec and -Wow! – this is easy math. Now calculate the distance you can run and the fire front moves in 10 secs intervals up to 1 minute.

mathspig-fire-fighter-table-4

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?

mathspig-cfa-diag-usa-units

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.

mathspig-fire-fighter-table-5

Now you can calculate the distance travelled up a slope at a 30º angle.

Don’t forget you can use the WEB 2.0 Calculator here

mathspig-fire-fighter-table-6

Even at your top running speed, which is unlikely up a slope, you can run 1080 ft in 1 minute. In that time the forefront has moved 8640 ft or 1.6 miles. It depends how far away you are from the fire front when you start running, but it seems likely that 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 70 mph 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 in a strong wind can reach 140 mph, 210 mph and up to 280 mph.

20o-angle-mathspig-2

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.

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3. STUNTMAN MATH: Motorbike Jump

October 9, 2019

This is a repost of Mathspig’s very popular Stuntman/woman series.

Star Stuntmen

Picture 2

Star Stuntmen Monte Perin (pictured) has involved many films, including “Spider-Man,” “Star Trek, “Indiana Jones and the Kingdom of the Crystal Skull” and portraying Arnold Schwarzenegger’s stunt double in “Terminator 3: Rise of the Machines.”

1. perlin_stunt_ Terminator 3

Perhaps his most difficult stunt was landing his Harley in an open boxcar of a moving train for Disney’s 2008 Adam Sandler movie “Bedtime Stories”. In a career of over 25 years Perin has broken “almost everything” including both his arms, legs, knees, feet, ankles, several ribs, his back and his pelvis. See Confessions of a stuntman

Veteran stuntman Evel Knievel (1938 – 2007) was the pioneer of many stunt jumps. Here he is jumping 10 cars and 3 vans in 1973.

2 Evel Knievel JUNE-23-1973

His injuries are legendary:

3 the-many-injuries-of-evel-knievel1

More Evel Knievel

Ramp Design

4 Ramp Design Angle of final kicker

The angle of the kicker in ramp design can vary from 100 – 700 (See below)

5 Robbie Maddison's 2008 New Year's Eve jump Arc de Triomphe at the Paris Las Vegas

Picture 2

 

Moto-X Ramp Jump Maths

6 motorbike -parabola Mr Reid

7 bike jump 1 Method 1



8 bike jump Method 1 final

 

9 bike jump method 1 final

 

Picture 2


10 bike jump method 1 final

 

As any bike nut knows increasing speed and angle of take off will increase jump distance.

Here is a graph from final gear for speed vs angle to jump 90m.

12 optimising ramp angle

 13bike jump Method 2

METHOD 1 is approximate (See STEP 1 & STEP 2 above), but as METHOD 2 produces the same ans (See above), it is very useful.

You will find a thoroughly detailed calc for STUNT JUMP MATHS here:

And everything you ever wanted to know about PHYSICS OF STUNT JUMPS here. 

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The Terrifying Maths of Running from a Bear … Metric Units

May 14, 2019

METRIC UNITS below. USA UNITS here.

BEAR STATISTICS

Grizzly Bear

Weight:   250kg

Height:   250cm

Top Speed: 56kph  =   16 m/sec

More bear stats here. 

Brown Bear

Weight:  680kg

Height:   250cm

Top Speed: 35kph  = 10m/s

More bear stats here.

Comparing these speeds to the fastest man on earth, Usain Bolt:

Usain Bolt:

Top speed: 243kph =   12m/s

So Usain Bolt could out run a Brown Bear but NOT a Grizzly!

Bears are NOT as dangerous as:

In fact more Americans die choking on their own vomit each year than a re killed by bears.

More death stats here.

But bears are very fast so Park Rangers recommend the following survival tactics:

More bear survival info here.

REF: Dog helps save hikers after grizzly chases them for 20 minutes here.

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1. You can duck a bullet

January 15, 2019

You will find all the ballistics stats you need here:

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2.You can out run a fireball?

January 14, 2019

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.