Question

A triathlete on the swimming leg of a triathlon is 130.0 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 130.2 m. Triathlete Water shoreline Land If the triathlete's running speed is 8.45 m/s and swimming speed is 1.267 m/s, calculate the value of x so that the triathlete reaches her bike in the least amount of time. Snell's Law is helpful here. Submit Answer Incorrect. Tries 1/12 Previous Tries Calculate the minimum time required to reach the bicycle. Submit Answer Tries 0/12

Answer 1

a)Total time taken = time of swimming + time of running

t = sqrt(a^2+x^2)/v1 + sqrt(y^2+b^2)/v2

t = sqrt(130^2+x^2)/1.267 + sqrt((130.2-x)^2+60^2)/8.45

For minimizing time, dt/dx = 0

We calculate this value using solver as x = 17.36 m answer

b) putting the value of x in t equation,

t = sqrt(130^2+17.36^2)/1.267 + sqrt((130.2-17.36)^2+60^2)/8.45

= 118.64 s answer