Shortest time to save the swimmer offshore (geometry) ?

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Homework Statement


Imagine a life guard situated a distance d1 from the water. He sees a swimmer in distress a distance L to his left and distance d2 from the shore. Given that his speed on land and water are v1 and v2 respectively, with v1 > v2, what trajectory should he choose to get to the swimmer in the least time? Pick some trajectory composed of two straight line segments in each medium (why?) and give a relation for the angles of the two segments with respect to the normal to the shoreline.

Homework Equations


Ha

The Attempt at a Solution


Should I include the diffraction of water, or should I not because this is a human? I'm assuming that I should use diffraction of water and so the corresponding optics equations because of the implication by "..some trajectory composed of two straight lines in each medium". If I didn't include diffraction, the angle wouldn't change, it would just be a straight line all the way through?
 
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Wait.. are his different velocities on and off shore going to be the cause of the different angles?
 
Vitani11 said:
Wait.. are his different velocities on and off shore going to be the cause of the different angles?
Yes, it is the reason for the two different angles. This is not a question of diffraction, it is simpler than that. Note that in each medium, th emotion must be a straight line.
 
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haruspex said:
Quite so - it is a question of refraction.
I did not want to give the solution outright so I did not mention refraction :-)

If your point is that refraction is an application of diffraction, I did not get into this because I did not think that the student was at a level of having seen how to prove refraction through Huygen's principle, I thought that by "diffraction" the OP was thinking about something quite separate from refraction. But I may have been wrong.
 
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Still in my first year of physics related courses so I'm not "polished". As a result I tend to mix things up like that. Anyway, thank you this has helped.
 
Suppose there is someone dumb like me who doesn't understand the relationship this problem has with optics (it appears to be a kinematics problem at first glance), how can it be solved without the optics approach?
 
Delta² said:
Suppose there is someone dumb like me who doesn't understand the relationship this problem has with optics (it appears to be a kinematics problem at first glance), how can it be solved without the optics approach?
What general rule governs the route light takes between two points?
 
haruspex said:
What general rule governs the route light takes between two points?

I guess it takes the route that it takes the shortest time to travel it among all other possible routes.