At a marine animal park, Alison is looking through a glass window and watching dolphins swim underwater. If the dolphin is swimming directly toward her at \(15 \mathrm{m} / \mathrm{s}\) how fast does the dolphin appear to be moving?

Short Answer

Expert verified
Answer: 15 m/s

Step by step solution

01

Identify the given information

In this problem, we are given the following information: - The dolphin is swimming towards Alison with a speed of \(15 \mathrm{m}/\mathrm{s}\). The goal is to find how fast the dolphin appears to be moving when Alison is watching it through the glass window.
02

Understand refraction in air, glass, and water

When Alison is looking at the dolphin through the glass window, light that is emitted or reflected from the dolphin must travel through water, glass, and air before reaching her eyes. At each boundary (water to glass and glass to air), the light gets refracted, meaning that its path bends and changes speed due to the difference in density between the two materials. The speed of light in a material is defined based on a property called the refractive index. The higher the refractive index, the slower the light travels, and the greater the bending. However, the problem does not give us enough information about the window or the water to account for refraction. This suggests that we should assume Alison's view of the dolphin's motion is not significantly distorted by the glass or the water.
03

Calculate the apparent speed of the dolphin

Given that we assume the view is not significantly distorted, we can say that the apparent speed of the dolphin is the same as its actual speed. Therefore, the dolphin appears to be moving at \(\boxed{15 \mathrm{m}/\mathrm{s}}\) as viewed by Alison.

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