Ant's Total Displacement Calculation

What is the total displacement of an ant that walks 2 meters west, 3 meters south, 4 meters east, and 1 meter north? Group of answer choices

2 meters east

All of the above.

2.8 meters south east

2 meters east and 2 meters south

To find the total displacement of the ant, we can break down its movements into components and then calculate the resultant displacement.

1. Movement Breakdown:

   • 2 meters west: This can be represented as (-2, 0).
   • 3 meters south: This can be represented as (0, -3).
   • 4 meters east: This can be represented as (4, 0).
   • 1 meter north: This can be represented as (0, 1).

2. Sum of Movements:

   • Total movement in the east-west direction: [ -2 + 4 = 2 \text{ meters east} ]
   • Total movement in the north-south direction: [ -3 + 1 = -2 \text{ meters south} ]

3. Resultant Displacement: The ant's total displacement can be represented as (2, -2), which means 2 meters east and 2 meters south.

4. Magnitude of Displacement: To find the magnitude of the displacement, we can use the Pythagorean theorem: [ \text{Magnitude} = \sqrt{(2^2) + (-2^2)} = \sqrt{4 + 4} = \sqrt{8} = 2.83 \text{ meters} ]

5. Direction: The direction can be found using the tangent function: [ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{2}{2} = 1 \implies \theta = 45^\circ ] This means the direction is southeast.

Based on the options provided, the correct answer is:

2 meters east and 2 meters south.