Archive for the ‘Decimals’ Category

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The Terrifying Maths of Running from a Bear … Metric Units

July 17, 2017

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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The Terrifying Math of Running from a Bear … USA Units

July 17, 2017

USA UNITS below. METRIC UNITS here.

BEAR STATISTICS

Grizzly Bear

Weight:  550 lb        

Height:  8’ 2”   

Top Speed: 35 mph  =   51 ft/s    

Brown Bear

Weight:  1,500 lb       

Height:  8’ 2”              

Top Speed: 22 mph  =  32 ft/s     

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

Usain Bolt:

Top speed: 27 mph  =   40 ft/s     

Bears are not dangerous:

………………………………………………………………………


In fact, more Americans die each year from choking on their own vomit than are killed by bears.

More death stats here

Nevertheless, bears are very fast. So you can see why Park Rangers offer the following advice:

More information at Mountain Nature.

The reason for waiting until the bear is 15 ft away is to make sure the spray doesn’t disperse in the air. If the Pepper Spray is too spread out it will not stop the bear.

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

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Smoke Jumpers and their Amazing Wildfire Maths . . . . . . . . . . . . . . METRIC UNITS

December 5, 2016

mathspig-smoke-jumpers 

With wildfires in Texas and now Australia is facing the fire season, it is time to think about fire fighter maths.

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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Smoke Jumpers and their Amazing Wildfire Maths . . . . . . . . . . . . . . USA UNITS

December 5, 2016

 

mathspig-smoke-jumpers 

With wildfires in Texas and now Australia is facing the fire season, it is time to think about fire fighter maths.

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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m+ms maths 7: how many m+ms will kill my pet mouse?

June 17, 2015

Maths topics 10

mathspig m&m maths 10

Theobromine is the poison found in chocolate. The LD50 is the Lethal Dose for 50% of animals to die. The LD50 information for mice can be found at The Toxicology Data Network

You can find more Death by Chocolate Maths here and here.

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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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1. Who uses more calories to travel 10 km: Mini or Man?

September 30, 2014

man vs mini 1a

Man vs mini 2a

Man vs mini 3a

ENERGY:

In Biodiesel

Consumed walking

In FAT including Human Fat