For an inverted pendulum near the top of its arc, there is no period, but the quantity √ℎ/𝑔 does represent a characteristic time scale for this system. The tree will take a few of these characteristic times to fall.

Mathspig hates seeing an old tree felled, but it does give us the necessary time data.

There are many assumptions in these calculations.

*You’d be hit by the tree trunk, not a branch which would hit you sooner.

*There is no wind pushing the tree over.

*The tree falling is an approx to a reverse pendulum.

When Mathspig recently saw images of some Russian soldiers covered in medals it prompted the question

‘Could medals protect the wearer from a sharpshooter?’

Mathspig was interested in this question because megalomaniac military dictators who take over countries by force tend to award themselves lots of medals. But they are also likely to be the target of sharpshooters from a liberation movement.

The target zone (circle) had a diameter of 1.9cm. This is smaller than the diameter of an American Quarter, an Australian 10c and a UK pound all of which have a diameter of appro 2.4 cm.

So the megolmaniac military dictator wins!!! He IS protected – on his chest – by his medals!!!!!! Unless the sharpshooter manages a ‘lucky’ shot.

When Mathspig recently saw images of some Russian soldiers covered in medals it prompted the question

‘Could medals protect the wearer from a sharpshooter?’

Mathspig was interested in this question because megalomaniac military dictators who take over countries by force tend to award themselves lots of medals. But they are also likely to be the target of sharpshooters from a liberation movement.

The target zone (circle) had a diameter of 0.7 inches. This is smaller than the diameter of an American Quarter, an Australian 10c and a UK pound all of which have a diameter of approx 0.96 inches.

So the megolmaniac military dictator wins!!! He IS protected – on his chest – by his medals!!!!!! Unless the sharpshooter manages a ‘lucky’ shot.

The follicle diagram (above) came from bgoffforensics blog. More on hair growth rates here.

QUESTION 1:

How long to grow that really bad 70s style hair cut?

The length of Fabio’s hair (below) is approx 50cm.

t = 50/1.25 months

t=40 months

t = 3 Years 4 months!!!!

Is it worth the effort? Ha!

QUESTION 2:

The growth rates of 1.25 cm/month or 0.5 inches/month are rounded off. Calculations using these growth rates will produce different answers for very large numbers (as above). Read more about the above story in the Daily Mail, UK here. By the way, Asha has been growing her hair for 25 years. Her hair weighs 3 stone or 19 kg. You can find more hair records including the World’s longest ear hair here.

QUESTION 3:

Natasha lives in Rio de Janeiro, Brazil. Read more about Natasha in the Daily Mail here. Once again Mathspig has rounded off the length of hair for easy calculation. The Daily Mail puts Natasha’s ‘mane’ at 5 feet 2 inches or 157 cm. This is the length of hair to be cut off. So Mathspig adjusted the length to 180cm or the approx length of her longest hair.

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.