A mouse in a maze scurries 41 cm south and then takes a 90-degree turn and scurries 64 cm west to get a piece of cheese. Find the mouse’s displacement
I know that the equation for displacement is
But I’m confused on where these numbers go in the equation
1. scientific theory
2. 0.24 lbs
3. starts with a problem or question
4. 76 cm southwest (the question u asked)
5. If the object moves in a straight line in one direction represented as positive then the magnitude of average velocity will be equal to the avg speed
6. 3 m/s^2
7. roughly 66.4 m
8. Weight, friction
9. Spring force
10. 12 n right
11. Wbrick- T sin theta
12. It increases
13. By increasing the normal force exerted by wood on the screw head
14. 2.5 m
15. -506,250 J
16. 60 kwh
17. The weather depends on too many conditions
21. 12 kgms
22. 3 J
23. Length 12 thickness 2
27. same amount of time
28. 22.3 AU
Ms. Sue is right 100%
In this case, the displacement of the mouse can be found using basic vector addition. We can break down the mouse's movement into two separate displacements: one in the south direction and the other in the west direction.
1. Southward displacement:
The mouse scurries 41 cm south. Since this is a straight line motion without any acceleration, we can directly assign this distance as the southward displacement: D₁ = 41 cm.
2. Westward displacement:
Next, the mouse takes a 90-degree turn and scurries 64 cm west. Again, since there is no change in direction and acceleration, we can assign this distance directly as the westward displacement: D₂ = 64 cm.
Now, we need to combine these two displacements (in the form of a vector) to find the overall displacement.
To do this, we will use the Pythagorean theorem:
Displacement (D) = √(D₁^2 + D₂^2)
Applying the values, we get:
D = √(41^2 + 64^2)
D = √(1681 + 4096)
D = √(5777)
D ≈ 76 cm
Hence, the mouse's displacement is approximately 76 cm.
To find the mouse's displacement, we can break down the motion into its components: one in the north-south direction and the other in the east-west direction.
Let's start by calculating the displacement in the north-south direction. The mouse scurries 41 cm south, which means it moves in the negative direction. Therefore, we assign a negative value to this displacement. Since there is no information about the time it took for the mouse to move this distance, we assume it was instantaneous. As a result, the equation for displacement in this case simplifies to D = -41 cm.
Next, we calculate the displacement in the east-west direction. The mouse scurries 64 cm west, which is also a negative displacement. Similarly, since we don't have information about the time taken, we assume it happened instantaneously. Thus, the equation for displacement in this case simplifies to D = -64 cm.
Now we have the displacement values for both the north-south component and the east-west component. To find the total displacement, we can use vector addition. Since these are in perpendicular directions, we can simply add the magnitudes and take into account the negative signs.
Displacement in the north-south direction: D1 = -41 cm
Displacement in the east-west direction: D2 = -64 cm
Total displacement: D_total = D1 + D2 = -41 cm + (-64 cm) = -105 cm.
So, the mouse's total displacement is -105 cm. The negative sign indicates that the displacement is in the opposite direction of the mouse's initial position. In this case, it means the mouse's final position is 105 cm south and 105 cm east from its starting point in the maze.