Carl, a mailman, is walking the neighborhood delivering mail. He walks 2 blocks east, then 3 blocks north, then 1 block west, then 3 blocks south. What is his displacement?
1 block East
To find the displacement of Carl, we need to calculate the net distance and direction from his starting point to his ending point.
Step 1: Convert each step into vector form, assuming each block is equal to one unit.
- Walking 2 blocks east ➝ +2i (east direction, no change in the vertical component)
- Walking 3 blocks north ➝ +3j (north direction, no change in the horizontal component)
- Walking 1 block west ➝ -1i (west direction, no change in the vertical component)
- Walking 3 blocks south ➝ -3j (south direction, no change in the horizontal component)
Step 2: Sum up the vectors to find the net displacement.
+2i +3j -1i -3j = +2i - 1i + 3j - 3j = +1i
Therefore, Carl's displacement is 1 block east.
To find Carl's displacement, we need to calculate the straight-line distance between his starting point and ending point. Displacement is a vector quantity that includes both the magnitude (distance) and direction.
To solve this problem, we can use a coordinate system where east is considered the positive x-direction and north is considered the positive y-direction.
Here's how we can calculate Carl's displacement step by step:
1. Start at the origin (0,0) on the coordinate plane.
2. Carl walks 2 blocks east, which means he moves 2 units in the positive x-direction. Now he is at point (2,0).
3. Next, Carl walks 3 blocks north, which means he moves 3 units in the positive y-direction. Now he is at point (2,3).
4. Carl walks 1 block west, meaning he moves 1 unit in the negative x-direction. Now he is at point (1,3).
5. Finally, Carl walks 3 blocks south, implying he moves 3 units in the negative y-direction. Now he is at point (1,0).
To calculate the displacement between the starting point and the ending point, we can use the distance formula:
displacement = √[(change in x)² + (change in y)²]
In this case, the change in x is 1, and the change in y is 0. Plugging these values into the formula, we get:
displacement = √[(1)² + (0)²]
displacement = √(1 + 0)
displacement = √1
displacement = 1
Therefore, Carl's displacement is 1 block in the positive x-direction (east).