To find the bunny's displacement, we can consider the two segments of its journey as vectors.
- The bunny first hops 20 meters north.
- Then it hops 8 meters west.
To calculate the resultant displacement, we can use the Pythagorean theorem. The northward hop represents one leg of a right triangle, and the westward hop represents the other leg.
Let:
- \( A \) = 20 meters (north)
- \( B \) = 8 meters (west)
The displacement \( D \) can be calculated as follows:
\[ D = \sqrt{A^2 + B^2} \]
Substituting the values:
\[ D = \sqrt{20^2 + 8^2} = \sqrt{400 + 64} = \sqrt{464} \]
Calculating \( \sqrt{464} \):
\[ D \approx 21.54 \text{ meters} \]
Now we can also find the direction of the displacement using the tangent function:
\[ \theta = \tan^{-1}\left(\frac{B}{A}\right) = \tan^{-1}\left(\frac{8}{20}\right) = \tan^{-1}(0.4) \]
Calculating \( \theta \):
\[ \theta \approx 21.8^\circ \text{ (west of north)} \]
Therefore, the bunny's displacement is approximately 21.54 meters at an angle of about 21.8 degrees west of north.
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