Translations:The principle of least time/7/en

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A lifeguard on the beach at A sees a drowning person in the water at E (Figure 9a). Which path should the lifeguard take to rescue the drowning person in the least time? The lifeguard might be tempted to take the straight-line path ACE because it represents the minimum distance he must travel. However, he knows that he can run faster on the beach than he can swim in the water. As a result, it pays to go a longer distance AD on the dry land to go a reduced distance DE in the water. Thus, by running to D and then swimming to E, the lifeguard does not minimize the distance he must travel, but he does minimize the time required to reach the drowning person. On the other hand, suppose the lifeguard were a seal. The seal waddles slowly on land but swims rapidly. The seal would take the path ABE. In fact, by instinct, a person in water will make a beeline for land, whereas a seal on land will make a beeline for water.