To determine the car's displacement from its starting point after traveling 30 meters east and then 40 meters north, we need to understand the concept of displacement and how to calculate it using the Pythagorean theorem. ### Step-by-Step Explanation 1. **Understanding Displacement**: - Displacement is a vector quantity that refers to the shortest distance from the initial position to the final position, along with the direction. It is different from distance, which is a scalar quantity that only considers how much ground is covered, regardless of direction. 2. **Visualizing the Movement**: - Imagine a coordinate system where the starting point of the car is at the origin (0,0). - When the car travels 30 meters east, it moves to the point (30,0). - Next, when it travels 40 meters north, it moves to the point (30,40). 3. **Finding the Displacement**: - The displacement can be visualized as the hypotenuse of a right triangle where: - One leg (the eastward movement) is 30 meters. - The other leg (the northward movement) is 40 meters. - We can use the Pythagorean theorem to find the length of the hypotenuse (displacement): \[ d = \sqrt{x^2 + y^2} \] where \(x\) is the distance traveled east (30 meters) and \(y\) is the distance traveled north (40 meters). 4. **Calculating the Displacement**: - Plugging in the values: \[ d = \sqrt{(30)^2 + (40)^2} \] \[ d = \sqrt{900 + 1600} \] \[ d = \sqrt{2500} \] \[ d = 50 \text{ meters} \] 5. **Conclusion**: - The car's displacement from its starting point is 50 meters in a direction that can be determined using trigonometry (specifically, the angle can be found using the tangent function, but that is not required for this question). ### Why the Other Options are Incorrect - **Option B (70 meters)**: This option incorrectly suggests that the total distance traveled (30 + 40 = 70 meters) is the displacement. Displacement is not simply the sum of the distances traveled in each direction; it is the straight-line distance from the starting point to the endpoint. - **Option C (30 meters)**: This option only considers the eastward movement and ignores the northward movement entirely. Displacement must account for both movements. - **Option D (40 meters)**: Similar to option C, this option only considers the northward movement and ignores the eastward movement. Again, displacement must consider both components. ### Common Pitfalls - Confusing distance with displacement: Remember that distance is a scalar quantity (total path length), while displacement is a vector quantity (shortest path from start to finish). - Forgetting to use the Pythagorean theorem when dealing with right triangles formed by movements in perpendicular directions. ### Revision Summary - Displacement is the shortest distance from the starting point to the endpoint, considering direction. - Use the Pythagorean theorem to calculate displacement when movements are at right angles. - The correct displacement for the car's journey is 50 meters. - Always differentiate between distance (scalar) and displacement (vector) in physics problems.