Final answer:
To find the resultant displacement of the train, we decompose each leg of the journey into north-south and east-west components, sum these components, and then calculate the magnitude and direction of the resultant using trigonometry and the Pythagorean theorem.
Step-by-step explanation:
A student has asked what the resultant displacement of a train is after it travels 150 km at 22° East of North, then travels 350 km at 82° South of West, and finally travels 225 km at 12° North of East. To solve this problem, we use vector addition. Each leg of the train's journey is represented as a vector, and we decompose these vectors into their north-south and east-west components. Here's how the calculation might look: First vector: 150 km at 22° East of North, Second vector: 350 km at 82° South of West, Third vector: 225 km at 12° North of East. After calculating the components, we sum up all the north-south components and all the east-west components to find the overall components of the resultant displacement vector. Then, we calculate the magnitude and direction of the resultant vector using trigonometry and Pythagorean theorem. Without actually performing these calculations, we cannot determine the correct option from the given choices of a. 415 km at 30° North of West, b. 305 km at 45° South of West c. 305 km at 45° North of West, d. 415 km at 30° South of West. Therefore, to find the resultant displacement, one would need to actually calculate each stage of the journey, combine the components, and then find the magnitude and direction of the result.