A triathlete on the swimming leg of a triathlon is 120.0 m from the shore ( a ).

Question

A triathlete on the swimming leg of a triathlon is 120.0 m from the shore (a). The triathlete's bike is 60.0 m from the shore on the land (b). The component of her distance from the bicycle along the shore line, ( x + y in the diagram), is 170.0 m.

1) If the triathlete's running speed is 9.15 m/s and swimming speed is 1.739 m/s, calculate the value of x so that the triathlete reaches her bike in the least amount of time.

2) Calculate the minimum time required to reach the bicycle.

Explanation / Answer

According to the question

given,

distance from the shore = 120 m

distance from the land = 60 m

distance between a and b = 170 m

time taken for swimming = distance / speed

time taken for swimming = (120^2 + x^2)^(1/2) / 1.739

time taken for running = (60^2 + (170- x)^2)^(1/2) / 9.15

total time taken = (120^2 + x^2)^(1/2) / 1.739+ (60^2 + (170- x)^2)^(1/2) / 9.15

finding minima for the above equation will get the answer.

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