# Enigmatic Code

Programming Enigma Puzzles

## Puzzle #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 100 mph.

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) 10 mph
b) 30 mph
c) 50 mph
d) 70 mph

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 100 km/h, the number in the solution will be the same.

[puzzle#25]

### One response to “Puzzle #25: Car crash maths”

1. Jim Randell 12 October 2019 at 8:28 am

If I remember correctly the kinetic energy of a body is proportional to the square of its velocity (mv²/2).

So the blue car, travelling at 7 speed units has 49 energy units.

And the yellow car, travelling at 10 speed units has 100 energy units.

They both start to brake at the exact same distance from the tree, and the blue car stops just short of the tree.

So assuming the brakes remove kinetic energy from the system at a constant rate they have removed 49 energy units from both cars. Enough to stop the blue car, but the yellow car still has 51 energy units left, so will hit the tree at just over 7 speed units. Which in this case is just over 70 mph.

Solution: (d) The yellow car hits the tree at about 70 mph.

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