If you travel 10 m [E], 25 m [S], 12 m [W] and 25 m [N], your displacement is
2 m west
Well, if I were to put on my math hat (or should I say clown nose?), I'd calculate your displacement by adding up the distances traveled in both the northern and eastern directions. So, traveling 10 m east and 25 m north, you end up with a displacement of 10 m [E], 25 m [N]. But who needs directions when you can just follow your gut and hope for the best?!
To calculate the displacement, you need to find the vector sum of the individual distances traveled in each direction. Displacement refers to the straight-line distance between the starting point and the final position. Here's how you can calculate it step-by-step:
1. Start by drawing a diagram to visualize the distances traveled in each direction. Assume your starting point is the origin (0, 0) on a coordinate plane.
2. Traveling 10 m to the east means moving 10 units to the right on the x-axis (+10, 0).
3. Then, travel 25 m to the south means moving 25 units down on the y-axis (+10, -25).
4. Moving 12 m to the west means moving 12 units to the left on the x-axis (-2, -25).
5. Finally, traveling 25 m to the north means moving 25 units up on the y-axis (-2, 0).
6. To calculate the displacement, find the straight-line distance between the starting point (0, 0) and the final position (-2, 0).
Using the distance formula:
Displacement = √[(x2 - x1)^2 + (y2 - y1)^2]
In this case, (x2, y2) = (-2, 0) and (x1, y1) = (0, 0).
Displacement = √[(-2 - 0)^2 + (0 - 0)^2]
Displacement = √[4 + 0]
Displacement = √4
Displacement = 2 meters.
Therefore, the displacement is 2 meters.
To calculate the displacement, we need to find the net distance and direction from the starting point to the ending point. Let's break down the given distances:
- Traveling 10 m [E] means moving 10 meters to the east.
- Traveling 25 m [S] means moving 25 meters to the south.
- Traveling 12 m [W] means moving 12 meters to the west.
- Traveling 25 m [N] means moving 25 meters to the north.
To find the net displacement, we need to combine these individual displacements.
First, let's consider the east and west directions. Since you traveled 10 m [E] and 12 m [W], the net displacement in the east-west direction would be 10 m - 12 m = -2 m. The negative sign shows that your net displacement is to the west.
Similarly, for the north and south directions, you traveled 25 m [S] and 25 m [N]. The net displacement in the north-south direction would be 25 m - 25 m = 0 m. As the net displacement is zero, it means there was no overall movement in the north-south direction.
Therefore, the displacement is -2 m [W].