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Which of the following sets of displacements might be capable of bringing a car back to its starting point?

1. 5, 10, 30 and 50 km
2. 5, 9, 9 and 16 km
3. 40, 40, 90 and 200 km
4. 10, 20, 40 and 90 km

Correct answer: 5, 9, 9 and 16 km

Solution

A set of displacements can bring an object back to the starting point only if they can form a closed polygon. This requires the largest displacement to be less than or equal to the sum of the others. For 5, 9, 9, 16, we have \(16 \le 5+9+9=23\), so it is possible.

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