A person walks in the following pattern: 2.9 km north, then 1.9 km west, and finally 8.0 km south. How far and in what direction would a bird fly in a straight line from the same starting point to the same final point?

Question

A person walks in the following pattern: 2.9 km north, then 1.9 km west, and finally 8.0 km south. How far and in what direction would a bird fly in a straight line from the same starting point to the same final point?

Answer 1

Add the displacements.

d=2.9km N + 1.9km W -8km N

then you have a N, and a W component.

direction=arc tan Ecomponent/Ncomponent (as measured clockwise from N).

magnitude: sqrt(N^2 + E^2)

Answer 2

To find the distance and direction the bird would fly in a straight line from the starting point to the final point, we can use the concept of vector addition.

First, let's represent the person's movements as vectors. A vector has both magnitude (distance) and direction. The person walks 2.9 km north, which we can represent as a vector "A" with a magnitude of 2.9 km and a direction of north. Similarly, the person walks 1.9 km west, which we can represent as vector "B" with a magnitude of 1.9 km and a direction of west. Finally, the person walks 8.0 km south, which we can represent as vector "C" with a magnitude of 8.0 km and a direction of south.

Now, we need to add these vectors together to find the net displacement of the person. Vector addition involves adding the magnitudes of the vectors in the respective directions.

To add vectors A and B, we can use the Pythagorean theorem: the magnitude of the resultant vector "R" is equal to the square root of the sum of the squares of the magnitudes of A and B.

Magnitude of R = sqrt((magnitude of A)^2 + (magnitude of B)^2)

Magnitude of R = sqrt((2.9 km)^2 + (1.9 km)^2)

Magnitude of R ≈ 3.47 km

The direction of the resultant vector R can be determined using trigonometry. We can use the tangent function to find the angle between vector A and vector B.

Angle = arctan((magnitude of B)/(magnitude of A))

Angle = arctan(1.9 km/2.9 km)

Angle ≈ 35.54°

So, the person's net displacement is approximately 3.47 km in a direction 35.54° west of north.

To find the distance and direction the bird would fly in a straight line from the starting point to the final point, we can use the magnitude and direction of the resultant vector R.

Therefore, the bird would fly approximately 3.47 km in a direction 35.54° west of north.