Optimizing Dolphin Tracking: Calculating the Angle for Dart Gun Accuracy

Click For Summary

Homework Help Overview

The problem involves calculating the angle at which a dart gun should be aimed to accurately hit a dolphin swimming underwater, considering the effects of refraction due to the water's refractive index. The scenario includes specific measurements of the scientist's height above water and the dolphin's depth.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of Snell's law and the implications of the angles involved in the refraction process. There are questions about the validity of the original poster's calculations and the interpretation of the ray diagram.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's reasoning and calculations. Some guidance has been offered regarding the interpretation of the ray diagram and the need to consider the straight path of the dart.

Contextual Notes

There are concerns raised about the realism of the scenario, particularly regarding the feasibility of the dart reaching the dolphin after impacting the water surface.

Seneka
Messages
41
Reaction score
0

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?
 

Attachments

  • spec_dolphin_underwater_s.png
    spec_dolphin_underwater_s.png
    28.4 KB · Views: 463
Physics news on Phys.org
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.
 
  • Like
Likes   Reactions: Seneka
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 ...