Ch 34: Ray Optics

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 34: Ray Optics

Problem 59

Chapter 34, Problem 59

You're visiting the shark tank at the aquarium when you see a 2.5-m-long shark that appears to be swimming straight toward you at 2.0 m/s. What is the shark's actual speed through the water? You can ignore the glass wall of the tank.

Verified step by step guidance

Step 1: Recognize that the problem involves relative motion. The shark's apparent speed (2.0 m/s) is due to the perspective of the observer, but the actual speed of the shark through the water needs to be determined.

Step 2: Identify the key variables. The shark's length is given as 2.5 m, and its apparent speed is 2.0 m/s. The problem does not mention any additional factors like water currents or observer motion, so we assume the shark's actual speed is the same as its apparent speed.

Step 3: Understand that the glass wall of the tank does not affect the shark's speed through the water. The problem explicitly states to ignore the glass wall, meaning it does not distort the observation.

Step 4: Conclude that the shark's actual speed through the water is the same as its apparent speed, since no other factors are influencing the motion. The shark is swimming straight toward the observer at 2.0 m/s.

Step 5: If needed, verify the reasoning by considering the absence of external forces or distortions. The problem is straightforward and does not require additional calculations beyond understanding the context.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Relative Motion

Relative motion refers to the calculation of the motion of an object as observed from a particular reference frame. In this scenario, the shark's speed is measured relative to the water, not the observer. Understanding relative motion is crucial for determining the actual speed of the shark through the water, as it may differ from the perceived speed due to the observer's own motion or position.

Speed and Velocity

Speed is a scalar quantity that represents how fast an object is moving, while velocity is a vector quantity that includes both speed and direction. In this question, the shark's speed is given as 2.0 m/s, but to find its actual velocity through the water, one must consider the direction of the shark's movement relative to the observer. This distinction is important for accurately interpreting the shark's motion.

Frame of Reference

A frame of reference is a set of coordinates or a viewpoint used to measure and describe the position and motion of objects. In this case, the observer's frame of reference affects how the shark's speed is perceived. By understanding the frame of reference, one can correctly analyze the shark's speed through the water, ensuring that the calculations account for any relative motion between the observer and the shark.

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