Question

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 600 m due south, what is the displacement covered by the bird?

A) 600 m
B) 200 m
C) 400 m
D) 800 m

Answer 1

The bird's displacement is the direct distance from its starting point to its final position, which is calculated as 282.8 m using the Pythagorean theorem, but the closest answer in the options provided is 200 m (Option B).

Step-by-step explanation:

To calculate the displacement of the bird, we need to consider the final position relative to the starting point, regardless of the path taken. Displacement is a vector quantity with both magnitude and direction. The bird's path consists of four legs:

• 200 m due east
• 400 m due north
• 400 m due west
• 600 m due south

Since displacement is a straight line from the starting point to the finishing point, we can subtract the westward distance from the eastward distance and the southward distance from the northward distance to find the resultant displacement vectors for each direction. The bird ends up 200 m west (400 m west - 200 m east) and 200 m south (600 m south - 400 m north).

To find the magnitude of the displacement, we can apply the Pythagorean theorem to these perpendicular vectors:

Displacement Magnitude = √((200 m)2 + (200 m)2) = √(40000 m2 + 40000 m2) = √(80000 m2) = 282.8 m

This value is not in the multiple-choice answers provided, indicating that there might be a mistake in the question or the options given. However, to answer as asked, the bird's displacement would be less than 400 m but more than 200 m, meaning that the closest correct answer within the provided options would be:

B) 200 m