Question

A hungry bunny rabbit hops 20 meters north and then turns and hops 8 meters west in search of tasty flowers to eat. what is the bunnies displacement

Answer 1

To find the bunny's displacement, we can consider the two segments of its journey as vectors.

1. The bunny first hops 20 meters north.
2. 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.