A bird watcher meanders through the woods, walking 1.07 km due east, 0.533 km due south, and 4.62 km in a direction 50.1 ° north of west. The time required for this trip is 1.451 h. Determine the magnitudes of the bird watcher's (a) displacement and (b) average velocity.
1.07 E = <1.07,0>
.533 S = <0,-0.533>
4.62 @ W50.1°N = <-2.963,3.644>
add them all up and you have a final displacement of
<-1.893,3.111> = 3.642 @ N31.3°W
now you can figure the velocity
To determine the magnitudes of the bird watcher's displacement and average velocity, we'll break down the given information into vectors and then calculate the necessary values.
Let's define the following vectors:
- Vector A: Represents the displacement of the bird watcher from the starting point to the endpoint of 1.07 km due east.
- Vector B: Represents the displacement of the bird watcher from the endpoint of Vector A to the endpoint of Vector B, which is 0.533 km due south.
- Vector C: Represents the displacement of the bird watcher from the endpoint of Vector B to the endpoint of Vector C, which is 4.62 km in a direction 50.1° north of west.
Now let's calculate the magnitudes of the displacement and average velocity:
(a) Magnitude of Displacement:
To calculate the magnitude of displacement, we need to find the resultant vector after adding all the individual vectors (A, B, and C).
To solve this, we'll use vector addition. The magnitude of displacement can be calculated as follows:
1. Add vectors A and B: Since A is in the east direction and B is in the south direction, the resultant vector will be the vector sum of A and B.
2. Add vector C to the resultant vector from step 1: Since C is in a direction north of west, you'll need to subtract this vector from the resultant vector obtained in step 1.
Once you have the resultant vector, you can calculate its magnitude.
(b) Magnitude of Average Velocity:
Average velocity is defined as the total displacement divided by the total time taken.
To calculate the magnitude of average velocity, divide the magnitude of displacement (calculated in step (a)) by the given time, which is 1.451 hours.
By following these steps, you should be able to determine the magnitudes of the bird watcher's displacement and average velocity.