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51. mmh On a safari, a team of naturalists sets out toward a research station located 4.8 km away in a direction 42° north of east. After trav- eling in a straight line for 2.4 km, they stop and discover that they have been traveling 22° north of east, because their guide misread his compass. What are (a) the magnitude and (b) the direction (relative to due east) of the displacement vector now required to bring the team to the research 0.81 21svat station?

51. mmh On a safari, a team of naturalists sets out toward a research station located 4.8 km away in a direction 42° north of east. After trav- eling in a straight line for 2.4 km, they stop and discover that they have been traveling 22° north of east, because their guide misread his compass. What are (a) the magnitude and (b) the direction (relative to due east) of the displacement vector now required to bring the team to the research 0.81 21svat station?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Physics Problem on Displacement Vectors #### Problem Statement: On a safari, a team of naturalists sets out toward a research station located 4.8 km away in a direction 42° north of east. After traveling in a straight line for 2.4 km, they stop and discover that they have been traveling 22° north of east, because their guide misread his compass. What are: (a) the magnitude and (b) the direction (relative to due east) of the displacement vector now required to bring the team to the research station? #### Analysis: This problem involves vector subtraction and trigonometry to find the new displacement vector needed for the team to reach their intended destination. 1. **Initial Displacement Vector (Desired Path)** - Distance: \(4.8 \, \text{km}\) - Direction: 42° north of east 2. **Actual Displacement Vector (Current Path)** - Distance: \(2.4 \, \text{km}\) - Direction: 22° north of east #### Solution Approach: - Represent both the desired and actual displacement vectors in Cartesian coordinates. - Subtract the actual displacement vector from the desired displacement vector to find the required displacement vector. - Calculate the magnitude and direction of this resultant vector. This problem demonstrates the practice of resolving vectors into components, using trigonometric functions for calculations, and understanding vector addition and subtraction in a real-world context. Feel free to use this problem to explore concepts in vector mathematics and its applications!
Transcribed Image Text:### Physics Problem on Displacement Vectors #### Problem Statement: On a safari, a team of naturalists sets out toward a research station located 4.8 km away in a direction 42° north of east. After traveling in a straight line for 2.4 km, they stop and discover that they have been traveling 22° north of east, because their guide misread his compass. What are: (a) the magnitude and (b) the direction (relative to due east) of the displacement vector now required to bring the team to the research station? #### Analysis: This problem involves vector subtraction and trigonometry to find the new displacement vector needed for the team to reach their intended destination. 1. **Initial Displacement Vector (Desired Path)** - Distance: \(4.8 \, \text{km}\) - Direction: 42° north of east 2. **Actual Displacement Vector (Current Path)** - Distance: \(2.4 \, \text{km}\) - Direction: 22° north of east #### Solution Approach: - Represent both the desired and actual displacement vectors in Cartesian coordinates. - Subtract the actual displacement vector from the desired displacement vector to find the required displacement vector. - Calculate the magnitude and direction of this resultant vector. This problem demonstrates the practice of resolving vectors into components, using trigonometric functions for calculations, and understanding vector addition and subtraction in a real-world context. Feel free to use this problem to explore concepts in vector mathematics and its applications!
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