#48 Seeing red
The traffic lights near me are annoying: they are green for just 10 seconds and red for 90 seconds. I go through them only on green on my bike every day and I first see the lights as I approach around a bend when I am 15 seconds away. I get upset if I miss a green light that I could have got through. I can speed up by about 25 per cent or I can slow down. What should my strategy be if the lights are green when I first see them? And what if they are red? And how often might I get upset?
Answer next week
#47 Geometra鈥檚 tomb
Solution
We are told that when Lees turns left (at position p) the distance to B (pB) is 100 kilometres further than the distance to C (pC, let鈥檚 call it 鈥淟鈥�). So pq = L.
Looking at the diagram, by symmetry Cp and Cq are the same, so the distance Cq is also L, so pqC is an equilateral triangle. So the angle by which Lees turns left is 60 degrees.
Quick quiz #40
1 A sidereal year is the time Earth takes to orbit the sun with respect to the stars, and a solar year is the time the sun takes to reach the same point in its annual cycle as seen from Earth. Which is currently longer?
2 What name is given to the phenomenon that causes this difference?
3 In England, which of these years had no 29 February: 1600, 1700, 1800, 1900, 2000?
4 Leap seconds are added to compensate for the drift of astronomical time from time marked out by atomic clocks. How many have been added since the first in 1972?
5 Atomic time is defined by what tiny sort of leap that in common parlance has come to mean a very big one?
Answers below
Quick quiz #40
Answers
1 Sidereal, by about 20 minutes
2 Precession of the equinoxes
3 1800 and 1900. The Gregorian calendar includes a leap year at turns of century divisible by 400; but England only adopted this in 1752
4 27
5 A quantum leap: specifically, the oscillation between energy levels of caesium-133 atoms