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The Maths in Greg Rutherford’s garden long-jump pit

Athletics has had a bad press recently, rightly so. But let’s celebrate one of Britain’s greats, Greg Rutherford, rightly nominated this week in the twelve for BBC Sports Personality of the Year

greg3Greg Rutherford’s fantastic long jump win at the World Championships meant he joined the select band of Brits holding the four major athletics titles at once. It was all the more fascinating because he has built a long- jump training pit in his back garden, as you can see below.

greg2Greg1

And a genuine GCSE Physics or Maths Higher tier question might be this: end of paper “tricky”, but in line with the emphasis on “real world problem solving”.

Question: Greg builds a long-jump run up and pit in his back garden.  He typically accelerates evenly from 0 to 10 metres per second in 4 seconds, then runs for 2 more seconds at 10m/s before take off. The world record leap is then approximately 9 metres and he allows another 3 metres for landing.  What is the minimum length Greg’s garden must be, from beginning of run up to end of landing?

Answer: in the first phase the word “evenly” implies a straight line velocity versus time graph from 0 to 4 seconds, and the distance covered is the area under that graph, namely half the base (2 seconds) times the height (10 m/s) i.e. 20 m.

The second phase at constant speed is simply speed x time equals distance i.e. 2 seconds x 10 m/s equals 20m.

The sand pit must be 9+3 = 12 m so the total minimum length is 20+20+12 equals 52m.

Finally, back to those awards: why no cricketer?! (Joe Root, genuine personality, Ashes winner, record number of international runs in a year!)

 

Foornote May 2016: Greg has actually announced a world class competiition in hos own back garden using the afore-mentioned long jump pit!