A fish directly beneath the surface of a lake sees a fly

[GreenPrint]

Homework Statement

A fish directly beneath the surface of a lake sees a fly on a stick above the water. The fish sees the fly at an angle of 36 degrees above the horizontal from it's current position and it's exactly .9 meters from the fish. At what angle must the fish spit a drop of water so that it hits the fly if the fly is to be it at the very top of the hyperbolic path taken by the drop of water spit by the fish?

The back of the book says 64.8 degrees. Is there a typo in the problem or something? I can't remember the exact wording of the question but it was something like this and the numbers are correct that I provided in the problem statement (I wrote down the numbers while listening to the problem being read). When I solved this question I got a imaginary number and not 64.8 degrees. Can anyone confirm that the answer is indeed 64.8 degrees?

Homework Equations

The Attempt at a Solution

 

[gneill]

Homework Statement

A fish directly beneath the surface of a lake sees a fly on a stick above the water. The fish sees the fly at an angle of 36 degrees above the horizontal from it's current position and it's exactly .9 meters from the fish. At what angle must the fish spit a drop of water so that it hits the fly if the fly is to be it at the very top of the hyperbolic path taken by the drop of water spit by the fish?

The back of the book says 64.8 degrees. Is there a typo in the problem or something? I can't remember the exact wording of the question but it was something like this and the numbers are correct that I provided in the problem statement (I wrote down the numbers while listening to the problem being read). When I solved this question I got a imaginary number and not 64.8 degrees. Can anyone confirm that the answer is indeed 64.8 degrees?

Something's fishy The critical angle for a ray passing from water to air is about 41.4° from the horizontal (or if you prefer, 48.6° from the vertical). Angles smaller than this will suffer total internal reflection. The fish shouldn't be able to see anything above the water that appears to have an angle as small as 36° to the horizontal. Could be a typo for that angle in the book.