Total Displacement Calculation for a Bird's Flight

What is the total displacement covered by the bird after its flight?

If a bird flew 200m due east, then turned and flew 400m due north, then turned and flew 400m due west, and turned again and flew 600m due south, what is the displacement covered by the bird?

Calculation of Total Displacement

The total displacement covered by the bird after its flight can be determined by calculating the sum of the individual displacements in each direction.

When a bird flies 200m due east, the displacement covered is +200m along the x-axis. When the bird then turns and flies 400m due north, the displacement is +400m along the y-axis. Subsequently, when it flies 400m due west, the displacement is -400m along the x-axis. Finally, when the bird flies 600m due south, the displacement is -600m along the y-axis.

To find the total displacement, we add up the individual displacements along the x-axis and the y-axis. The bird's total displacement would be (-400m) + (+200m) = -200m along the x-axis and (-600m) + (+400m) = -200m along the y-axis. Therefore, the bird's total displacement is -200m in the x-direction and -200m in the y-direction.

By using the Pythagorean theorem to calculate the magnitude of the total displacement: sqrt((-200m)^2 + (-200m)^2) = 282.8m. Hence, the total displacement covered by the bird after its flight is approximately 282.8m.

For further information on displacement calculations, refer to reliable sources and study materials related to physics and vector operations.