Problem 1.6.10. Imagine a life guard situated a distance dı from the water. He sees a swimmer in distress a distance L to his left and distance d2 from the shore. v1 > 02. what trajectory will get him to the swimmer in the least time? Does he rush towards the victim in a straight line joining them, does he first run on land until he is in front of the victim and then swim, does he head for the water first and then swim Given that his speed on land and water are vị and v2 respectively, with line segments in each medium (why) and show that for the least time sin 6 where the angles O; are the angles of the segments with respect to the normal over, or does he do something else? Pick some trajectory composed of two stret sin 02 %3D U2 the shoreline. This problem has an analog in optics. If light is emitted at a point in a medium where its velocity is vi and arrives at a point in an adjacent medium where in velocity is v2, the route it takes is arrived at in the same fashion since light takes the path of least time. The above equation is called Snell's Law.

Problem 1.6.10. Imagine a life guard situated a distance dı from the water. He sees a swimmer in distress a distance L to his left and distance d2 from the shore. v1 > 02. what trajectory will get him to the swimmer in the least time? Does he rush towards the victim in a straight line joining them, does he first run on land until he is in front of the victim and then swim, does he head for the water first and then swim Given that his speed on land and water are vị and v2 respectively, with line segments in each medium (why) and show that for the least time sin 6 where the angles O; are the angles of the segments with respect to the normal over, or does he do something else? Pick some trajectory composed of two stret sin 02 %3D U2 the shoreline. This problem has an analog in optics. If light is emitted at a point in a medium where its velocity is vi and arrives at a point in an adjacent medium where in velocity is v2, the route it takes is arrived at in the same fashion since light takes the path of least time. The above equation is called Snell's Law.