Calculation of The Bird Watcher's Displacement and Average Velocity
A bird watcher meanders through the woods walking 1.24 km due east, 1.23 km due south, and 3.89 km in a direction 68.2 degrees north of west. The time required for this trip is 2.313 hours. Let's determine the magnitudes of the bird watcher's:
- (a) Displacement
- (b) Average Velocity
What is the method to find the bird watcher's displacement and average velocity?
To find the bird watcher's displacement, each displacement vector is broken down into its components and added together. The Pythagorean theorem is then used to calculate the magnitude of the displacement. For the average velocity, displacement is divided by total time.
The bird watcher's displacement can be calculated by using the Pythagorean theorem in 2D. From the origin, first 1.24 km is covered due east, then 1.23 km due south, and finally 3.89 km in a direction 68.2 degrees north of west. Therefore, the displacement is the magnitude of the resultant of these three vectors. Let's take east and north as positive.
So, we will have:
X = 1.24 (east) - 3.89 * cos(68.2) (part of the bird watcher's third displacement to the west)
Y = 3.89 * sin(68.2) (part of the bird watcher's third displacement to the north) - 1.23 (south)
After calculating X and Y elements, the total displacement can be found as sqrt(X^2 + Y^2).
For the average velocity, it is displacement divided by total time, as velocity is a vector quantity and its average would still point in the direction of the displacement. Mathematically, Average velocity = Displacement / Total Time.