………………………………………….
You have 2 parents, 4 grandparents, 8 great grandparents, ETC, ETC
The no. of ancestors you have per generation follows an EXPONENTIAL FUNCTION:
Here are the numbers going back 50 generations or 1,000 years.
When you plot YOUR NO. ANCESTORS over a POPULATION OF THE WORLD GRAPH there is a problem.
Population of the World DATA HERE
If you look at the graph (above) you will see that the No. YOUR ANCESTORS equalled the POPULATION OF THE WORLD about 500 years or 25 Generations ago.
You are related to everyone who was alive 500 years ago. Some of your ancestors inlcude:
Of course, EVERYONE else has these ancestors too.
If you go back 50 generations you have more ANCESTORS than the entire POPULATION OF THE WORLD.
Anthropologists say that there was a lot of IN BREEDING especially when humans lived in small tribes and the world population was small.
So way back every one of our family trees has members popping up all over the place. So we had far fewer ancestors than the math suggests.
Here are just a few of the popular disaster movies:
Avalanche (2001), Earthquake (1974), Armageddon (Involves meteors 1998), Deep Impact (More meteors 1998), 2012 (Tsunamis, earthquakes, the lot. 2009), Twister (tornadoes 1996), Backdraft (Fire. 1991) and Towering Inferno (They don’t make thunderous movie titles like that anymore. (1974)
But what percentage of people involved in, say, an explosion suffer from SHOCK! There are many statistics about Post Traumatic Stress Disorder (PTSD) available. In one excellent study in The National Centre for PTSD Journal involved an explosion in a paint factory in Norway (1976), the 246 employees were ranked for their exposure to shock as follows:.
A. 66 Narrow escape
B. 59 Involved but not in danger
C. 121 Not present on the day.
80% Group A suffered shock and PTSD. Both Groups A & B showed symptoms of PTSD 7 months later. If, say, a plane crashed into your school sports field and your class survived with minor injuries calculate how many students in your maths class would go into SHOCK and how many would be left to take action using the above statistics.
These stats can also be used as a fraction or decimal exercise using 0.8 or 4/5 as the fraction of students in shock.
More information at the Health Dept WA
NOTE: Many schools in Australia today not only practise fire drills but terrorist attack lockdowns.
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.
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.
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.
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
The likelihood of a passenger with
This is a rework of a previous post with full calcs.
Every volcano disaster movie from Volcano (1997) with Tommy Lee Jones to Dante’s Peak (1997) with Pierce Brosnan someone somewhere tries to out run a lava flow. Is this possible?
The answer is maybe. You will find everything you want to know about lava flows here.
On January 10,1977, at Nyiragongo lava sprang from the sides of the volcano moving at speeds up to 40 miles per hour. About 70 people were killed.
Measuring the temperature of lava. Photograph by R.L. Christiansen, U.S. Geological Survey, January 9, 1973.
The fastest Lava flows recorded were in Hawaiiin 1950 when Mauna Loa erupted. The lava traveled at 6 miles per hour through thick forest. But once the lava flows became established and good channels developed, the lava in the channels was flowing at up to 60 mph.
Speed of average sprinter = 10 – 15 mph
With wildfires burning across the US and Europe , Mathspig had to update this firefighter math for middle school classrooms.
Radiant Heat Stats WA Fire Dept FACEBOOK.
Wildfires USA 2022 Map:NASA
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.
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
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
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.
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.
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 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 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.
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.
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.
With wildfires burning across the US and Europe , Mathspig had to update this firefighter maths post for middle school classrooms.
Radiant Heat Stats WA Fire Dept FACEBOOK, Australian Bushfires 14 NOV 2019 MyFireWatch WA
Wildfires USA 2022 Map: NASA
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.
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
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
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.
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.
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.
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.
A raucous romp through the absurdities of American Gun Culture
10 Reasons Students Hate Maths: BUSTED
10 Reasons Students Hate Maths: BUSTED
10 Reasons students hate maths: BUSTED
10 Reasons Why Students Hate Maths: BUSTED
10 Reasons students Hate Maths: BUSTED
10 reasons to hate maths: BUSTED
10 reasons to hate maths: BUSTED
10 reasons to hate maths: BUSTED
10 Reasons to Hate Maths: BUSTED
10 Reasons to Hate Maths: BUSTED
Comic & cutting comment plus random raves.
Mathspig Blog 
