Questions: Multiple Choice Question 1.22 A bird flies 3.4 km due west and then 1.6 km due north. Part A What is the magnitude of the bird's displacement? 1.6 km 3.4 km 3.8 km 5.0 km Submit Request Answer Provide Feedback

Solution Steps

The bird flies 3.4 km due west and then 1.6 km due north. These are the components of the bird's displacement in the west and north directions, respectively.

To find the magnitude of the bird's displacement, we use the Pythagorean theorem. The displacement forms a right triangle with the west and north components as the legs.

\[ \text{Magnitude} = \sqrt{(3.4 \, \text{km})^2 + (1.6 \, \text{km})^2} \]

Calculate the squares of the components:

\[ (3.4 \, \text{km})^2 = 11.56 \, \text{km}^2 \] \[ (1.6 \, \text{km})^2 = 2.56 \, \text{km}^2 \]

Add these values:

\[ 11.56 \, \text{km}^2 + 2.56 \, \text{km}^2 = 14.12 \, \text{km}^2 \]

Take the square root to find the magnitude:

\[ \sqrt{14.12 \, \text{km}^2} \approx 3.755 \, \text{km} \]

Final Answer