Question

A hungry bunny rabbit hops 20 meters north and then turns and hops 8 meters west in search of tasty flowers to eat. and show the work in a simple way

Answer 1

To find the total distance the bunny has moved and its final position, we can break down the steps of its movement.

### Step 1: Analyze the Movement

1. **First Movement**: The bunny hops 20 meters north.
2. **Second Movement**: The bunny then hops 8 meters west.

### Step 2: Visualizing the Path

If we visualize the bunny's path on a coordinate plane:
- Start at point (0, 0).
- After moving 20 meters north (upward on the y-axis), the bunny is now at point (0, 20).
- After moving 8 meters west (left on the x-axis), the bunny's new position is (-8, 20).

### Step 3: Calculate the Total Displacement

To find the straight-line distance from the starting point (0, 0) to the final position (-8, 20), we use the Pythagorean theorem:

\[
\text{Distance} = \sqrt{(x^2 + y^2)}
\]

Where:
- \( x \) is the horizontal movement (west) = -8 meters
- \( y \) is the vertical movement (north) = 20 meters

Plugging in the values:

\[
\text{Distance} = \sqrt{(-8)^2 + (20)^2}
\]

Calculating:

\[
\text{Distance} = \sqrt{64 + 400}
\]
\[
\text{Distance} = \sqrt{464}
\]
\[
\text{Distance} \approx 21.54 \text{ meters}
\]

### Final Summary

- **Total Distance Traveled**: The bunny hops a total of \( 20 + 8 = 28 \) meters.
- **Straight-Line Displacement**: The bunny's displacement from its starting point to its final position is approximately **21.54 meters** in the northwest direction.

This gives you the total movement and a clear understanding of the bunny’s path!