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Puzzle for Today

Puzzle No. 434 – Tuesday 12 March

A chilly BBC presenter stands on one side of a 100 meter wide fjord in Svalbard. Directly opposite sits a polar bear. Knowing a polar bear can swim at 10 kilometres per hour, and the water surface current is flowing at 8 kilometres per hour, what is the quickest time in which the polar bear can reach the presenter?

Today’s #PuzzleForToday has been set by Dr Geoff Evatt, School of Mathematics, University of Manchester

1 minute! This is because the quickest path is to go straight across. In order to do that, the bear must swim at an angle into the current. With the resultant velocity towards the reporter being straight across the fjord, and the current flowing at right angles to the banks, one can use Pythagoras' theorem (adjacent length squared + opposite length squared = hypotenuse length squared) to find the size of the resultant velocity. Here the hypotenuse is 10kph (relative to the surface, the bear always swims at 10kph), and the opposite velocity is the current, given by 8kph, making the adjacent velocity towards the reporter 6kph. This means the bear could swim 1km in 10 minutes, and thus 100m in 1 minute. For clarity, whilst the bear velocity is realistic, the current velocity is right at the upper end of possible.

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