A mouse runs 5 m north across the floor before hearing a cat. Then it runs back south along the same path for 1 m and turns west to run under a sofa 3 m away. what is the displacement of the mouse and the total distance it ran
To find the displacement, we need to find the net distance and direction from the starting point to the final position of the mouse.
The mouse runs 5 m north, then runs back 1 m south, so the net distance in the north-south direction is 5 m - 1 m = 4 m south.
Then, it turns west and runs 3 m under the sofa, so the distance in the west direction is 3 m.
Since the mouse did not move in the east direction, the displacement in the east-west direction is 0 m.
Therefore, the displacement of the mouse is 0 m (east-west) + 4 m (north-south) = 4 m south.
To find the total distance, we need to sum up all the distances traveled.
The mouse runs 5 m north + 1 m south + 3 m west, so the total distance is 5 m + 1 m + 3 m = 9 m.
Therefore, the displacement of the mouse is 4 m south, and the total distance it ran is 9 m.
To calculate the displacement of the mouse, we need to find the straight-line distance between its starting point and ending point. We can use the Pythagorean Theorem to do this.
The mouse ran 5 m north and then 1 m south, which cancels out to a net northward distance of 4 m.
Then, the mouse turns west and runs under a sofa 3 m away.
Using the Pythagorean Theorem, we can find the displacement:
displacement = √(4^2 + 3^2)
= √(16 + 9)
= √25
= 5 m
So, the displacement of the mouse is 5 m.
To find the total distance the mouse ran, we can sum up the individual distances traveled:
Total distance = distance north + distance south + distance under the sofa
= 5 m + 1 m + 3 m
= 9 m
Therefore, the total distance the mouse ran is 9 m.
To find the displacement of the mouse, we need to calculate the straight-line distance between the starting point and the final position.
First, let's break down the movements of the mouse:
1. The mouse runs 5 m north.
2. It then runs 1 m south.
3. Finally, it turns west and runs 3 m under the sofa.
To find the displacement, we can determine the horizontal and vertical distances traveled by the mouse separately.
Horizontal distance:
The mouse runs 3 m west under the sofa.
Vertical distance:
The mouse initially runs 5 m north and then runs 1 m south. Therefore, the vertical distance traveled is 5 m - 1 m = 4 m north.
Now, we can use the Pythagorean theorem to find the displacement since the distance traveled along the horizontal and vertical axes form a right triangle.
Displacement = √(horizontal distance)^2 + (vertical distance)^2
Displacement = √(3 m)^2 + (4 m)^2
Displacement = √(9 m^2 + 16 m^2)
Displacement = √(25 m^2)
Displacement = 5 m
So, the displacement of the mouse is 5 m. This represents the straight-line distance between the starting point and the final position.
To find the total distance the mouse ran, we need to add up the distances traveled during each segment:
Distance = distance north + distance south + distance west
Distance = 5 m + 1 m + 3 m
Distance = 9 m
Therefore, the total distance the mouse ran is 9 m.