a bee flies 12m north, 8m west, and then 4m south, what is the displacement
8 m north and 8 m west, when added as vectors, has a magnitude of
sqrt(8^2 + 8^2) = 8 sqrt2 = 11.314 m
is this the formula R^2= X^2+Y^2
physiscs is butt
To find the displacement of the bee, we need to calculate the straight-line distance from the starting point to the ending point. Displacement is a vector quantity and is the shortest distance between two points, regardless of the path taken.
In this case, the bee first flies 12m north, then 8m west, and finally 4m south. Let's visualize this on a coordinate plane. Assuming the starting point is the origin (0, 0), we can represent the movements as follows:
- The bee moves 12m north, so it ends up at (0, 12).
- Next, it moves 8m west, so it ends up at (-8, 12).
- Finally, it moves 4m south, so it ends up at (-8, 8).
To find the displacement, we need to find the straight-line distance between the starting point (0, 0) and the ending point (-8, 8). We can use the Pythagorean theorem to calculate this:
Displacement = √[(change in x)² + (change in y)²]
In this case, the change in x is -8 - 0 = -8, and the change in y is 8 - 0 = 8. Plugging these values into the formula:
Displacement = √[(-8)² + 8²]
= √[64 + 64]
= √128
≈ 11.31
Therefore, the displacement of the bee is approximately 11.31 meters.