Shortest time to save the swimmer offshore (geometry) ?

[Vitani11]

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?

 

[Vitani11]

Wait.. are his different velocities on and off shore going to be the cause of the different angles?

 

[nrqed]

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.

 

[haruspex]

This is not a question of diffraction

Quite so - it is a question of refraction.

 

[nrqed]

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.

 

[Vitani11]

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.

 

[Delta2]

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?

 

[haruspex]

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?

 

[Delta2]

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.

 

[haruspex]

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

Rght.