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!