triathlete on the swimming leg of a triathlon is 150.0 m from the shore (a). The

Question

triathlete on the swimming leg of a triathlon is 150.0 m from the shore (a). The triathletes bike is 60.0 m m the shore on the and (b). The component of her distance from the bicycle along the shore line, x y in the diagram), is 149.0 m. Triathlete Water shoreline Land If the triathlete's running speed is 9.05 m/s and swimming speed is 1.720 m/s, calculate the value of x so that the triathlete reaches her bike in the least amount of time 87.60 m Snell's Law is helpful here. Submit Answer Incorrect. Tries 4/12 Previous Tries Calculate the minimum time required to reach the bicycle Submit Answer Tries 0/12

Explanation / Answer

a] By Snells law, n1 sin theta1 = n2 sin theta2

n1/n2 sin theta1 = sin theta2

9.05/1.72 * x/sqrt(a^2+x^2) = y/sqrt(b^2+y^2)

(9.05/1.72) * x/sqrt(150^2+x^2) = (149-x)/sqrt(60^2+(149-x)^2)

solving the quadratic equation with calculator, x = 26 m answer

b] time t = sqrt(150^2+26^2) /1.72 + sqrt(60^2+(149-26)^2)/9.05

= 103.6 s answer

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