To find the displacement of the mouse and the total distance it ran, let's analyze the movements step-by-step.
- Initial Movement (North): The mouse runs 5 meters north.
- Second Movement (South): The mouse then runs back 1 meter south. The net northward movement is \(5 m - 1 m = 4 m\) north.
- Third Movement (West): Finally, the mouse runs 3 meters west.
Now, to calculate the total distance run, we sum all the distances traveled:
- First leg: 5 m (north)
- Second leg: 1 m (south)
- Third leg: 3 m (west)
Total distance = \(5 m + 1 m + 3 m = 9 m\).
Next, we calculate the displacement, which is the straight-line distance from the starting point to the endpoint. The mouse is now 4 m north and 3 m west of its starting point.
Using the Pythagorean theorem to find the displacement:
\[ \text{Displacement} = \sqrt{(4 m)^2 + (3 m)^2} = \sqrt{16 + 9} = \sqrt{25} = 5 m. \]
To determine the direction of the displacement, we can use trigonometry:
- The angle \(\theta\) can be found using:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{3 m}{4 m}. \]
The angle points in the northwest direction since the mouse is north but also moves west. Therefore, the displacement is 5 m in the northwest direction.
In summary:
- The total distance the mouse ran is 9 m.
- The displacement of the mouse is 5 m northwest.
Based on the options provided: The mouse's displacement is 5 m northwest and it ran 9 m.
1 answer