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Answer :
Final answer:
The net displacement of a fish that swims 50 m due east and then 150 m northwest can be found using vector addition. The magnitude and direction are calculated using the component method involving the Pythagorean theorem and trigonometric functions to add vectors.
Explanation:
The student asked about the net displacement of a fish that travels 50 m due east and then 150 m northwest at a 45° angle north of west. To find the fish's net displacement, one can use the method of vector addition, where the individual displacements are treated as vectors and added using their x and y components. The fish's eastward movement only has an x component (positive), while the northwest movement has both x (negative) and y (positive) components.
By breaking the northwest vector into its components using trigonometric functions (cosine and sine for x and y components, respectively), and summing the x and y components of both movements, we can find the resultant vector. The magnitude of the resultant vector gives us the net displacement in meters, while the direction can be found by taking the arctangent of the y component over the x component.
The net displacement of a vector can be calculated using the Pythagorean theorem to find the magnitude and inverse trigonometric functions for the direction. For the given example, the correct answer using this method would involve calculating the x and y components of the 150 m vector as follows: 150 m ∙ cos(45°) = 106.1 m (westward) and 150 m ∙ sin(45°) = 106.1 m (northward), then adding these to the initial 50 m eastward vector to get the final displacement vector.
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