What is the total distance and displacement when Maria walks 3 m north and then 4 m east to get to the kitchen from her bedroom?
The total distance Maria walks is calculated by adding the individual distances in each direction. In this case, Maria walks 3 meters north and then 4 meters east, so the total distance is 3 + 4 = 7 meters.
Displacement, on the other hand, is the shortest distance between Maria's starting point and her destination. To calculate displacement, we can use the Pythagorean theorem. We square the distances walked in each direction, add them, and then take the square root of the sum.
Using Pythagoras theorem: square root (3^2 + 4^2) = square root (9 + 16) = square root (25) = 5 meters.
Understanding Distance and Displacement
In this scenario, Maria's movement from her bedroom to the kitchen involves walking 3 meters north and 4 meters east. These two movements form a right triangle, with the distances walked being the legs of the triangle.
Distance is the total length of the path traveled by Maria. When we calculate the distance, we simply add the individual distances in each direction together. In this case, it is 3 meters north + 4 meters east = 7 meters.
Displacement, on the other hand, is the straight-line distance between Maria's starting point (her bedroom) and her destination (the kitchen). To find the displacement, we treat the northward and eastward movements as the two perpendicular sides of a right triangle. Using the Pythagorean theorem, we can calculate the hypotenuse (the displacement) as the square root of the sum of the squares of the two legs.
By squaring and adding the distances walked north and east: 3^2 + 4^2 = 9 + 16 = 25. Taking the square root of 25 gives us the displacement: √25 = 5 meters. This means that Maria's displacement from her bedroom to the kitchen is 5 meters, which is the shortest distance between the two points.
In conclusion, while the total distance Maria walks is 7 meters, her displacement is 5 meters. Understanding the concepts of distance and displacement is essential in physics, navigation, and various other fields where precise measurements and calculations are required.