To calculate the average velocity, we first need to determine the total displacement as well as the total time taken for the walk.
Step 1: Calculate total displacement.
- You walk 800 m North, 600 m East, and then 200 m South.
- The net movement in the North-South direction is: \(800 \text{ m North} - 200 \text{ m South} = 600 \text{ m North}\).
- The movement in the East-West direction is: \(600 \text{ m East}\).
Now, we can find the resultant displacement using the Pythagorean theorem:
\[ \text{Displacement} = \sqrt{(600 \text{ m})^2 + (600 \text{ m})^2} = \sqrt{360000 + 360000} = \sqrt{720000} = 600\sqrt{2} \approx 848.53 \text{ m} \]
Step 2: Calculate total time taken.
- The total distance walked is: \[ 800 \text{ m} + 600 \text{ m} + 200 \text{ m} = 1600 \text{ m} \]
- The speed is 1 m/s, hence the total time taken is: \[ \text{Total Time} = \frac{\text{Total Distance}}{\text{Speed}} = \frac{1600 \text{ m}}{1 \text{ m/s}} = 1600 \text{ seconds} \]
Step 3: Calculate average velocity.
- Average velocity is defined as total displacement divided by the total time taken:
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{848.53 \text{ m}}{1600 \text{ s}} \approx 0.5303 \text{ m/s} \]
Now, let's find the vector components of the average velocity:
- The average velocity can be resolved into North and East components based on total displacement:
- The North component (\(V_N\)): \[ V_N = \frac{600}{1600} = 0.375 \text{ m/s} \]
- The East component (\(V_E\)): \[ V_E = \frac{600}{1600} = 0.375 \text{ m/s} \]
Conclusion: The average velocity vector can thus be represented as: \[ \text{Average Velocity} = 0.375 \text{ m/s North} + 0.375 \text{ m/s East} \]
Thus, the correct answer is: \[ \text{0.375 m/s North + 0.375 m/s East} \]
2 answers