Optimizing Dolphin Tracking: Calculating the Angle for Dart Gun Accuracy

AI Thread Summary
The discussion focuses on calculating the angle at which a scientist should aim a dart gun to accurately hit a dolphin swimming 2m below the surface while standing 1m above the water. Using Snell's law, the initial calculation determined the angle in water to be 32 degrees, but the subsequent steps to find the angle above water were incorrect. The error arose from misunderstanding how to treat the rays as vectors and the need to find the straight path of the dart rather than reproducing the bent line in the ray diagram. Participants noted the unrealistic nature of the scenario, questioning whether the dart would even reach the dolphin after impacting the water. Accurate calculations and understanding of refraction are crucial for solving this problem effectively.
Seneka
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Homework Statement


A scientist investigating the movements of dolphins in the Mediterranean uses a dart gun to shoot small, harmless tracking devices onto the fins of dolphins. When standing on deck, her hand is 1m above the water, and looking along the dart gun she is holding at an angle of 45∘, she sees a dolphin. Using sonar she has found that the dolphin is swimming at a depth of 2m. We know that the refractive index for water is 1.33. At what angle from the horizontal should she point the dart gun to hit the dolphin?

Homework Equations


n1sintheta1=n2sintheta2
Answer:
spec_dolphin_underwater_s.png


The Attempt at a Solution


I worked out the angle in the water to be 32 degrees using the equation above and extended that line from the dolphin to the refracted ray above the water to the scientists hand. I knew that this would make an angle of 180 degrees so I subtracted 32 and 90 from 180 to give me 58 degrees as the answer. This is wrong but I don't understand why. Why do you treat the the two rays as vectors and why do you add them? What is wrong with my working out?
 

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Seneka said:
and extended that line from the dolphin to the refracted ray above the water to the scientists hand.
That sequence does not produce a straight line, it merely reproduces the bent line in the ray diagram.
The task is to find the angle of the straight path the dart will take.
 
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haruspex said:
That sequence does not produce a straight line, it merely reproduces the bent line in the ray diagram.
The task is to find the angle of the straight path the dart will take.
Cool, thanks
 
This problem seems very unrealistic and completely ignores whether or not that dart would actually be able to reach the dolphin after impacting on the water surface ...
 
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