#25: Car crash maths
Two cars of the same model, one blue, one yellow, are on a motorway in the UK. The blue car is in the inside lane travelling at 70 miles per hour*, which is the speed limit. The yellow one is speeding in the outside lane at 100mph.
At the instant when they are neck and neck, both drivers see a fallen tree across the road some distance ahead. Both immediately brake, each applying the same constant braking force. The blue car manages to stop centimetres short of the tree. To the nearest 10mph, at what speed does the yellow car hit the tree?
a) 10mph
b) 30mph
c) 50mph
d) 70mph
Use your intuition (particularly if you are a driver) to have a guess. Then work out the answer to see if you were right.
* Alternatively, call the starting speeds 70 kilometres per hour and 100km/h, the number in the solution will be the same.
Answer next week
#24 Three stamps
Solution
a) To allow all postage values up to 15 cents using no more than three stamps, the choice of 1垄and 5垄stamps is obvious. That leaves the values 4, 8, 9, 12, 13 and 14 unaccounted for, which can be solved by choosing 4垄as the third stamp. So you need to choose 1垄, 4垄and 5垄 stamps.
b) To make all postage values to 24垄 with four stamps or less, choosing 1垄, 4垄and 8垄stamps is sensible. To cover the values not possible with those, the fourth stamp must be 7垄.
Quick Quiz #24
1 What name is given to the sudden appearance of most animal lineages in the fossil record starting around 541 million years ago?
2 Soft body parts fossilised in which rock formation in the Canadian Rockies are crucial to understanding that sudden shift in life on Earth?
3 Which US palaeontologist and science populariser鈥檚 1989 book Wonderful Life brought those Canadian fossils to wider attention?
4 What name, referring to their three major body sections, is given to an extinct group of marine arthropods characteristic of the period in question?
5 What dismissive name is sometimes given to a long period of apparent stasis in evolution, starting around 1.8 billion years ago, before the emergence of animals?
Answers below
Quick quiz #24
Answers
1 The Cambrian explosion
2 The Burgess Shale
3 Stephen Jay Gould
4 Trilobites
5 The boring billion
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