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
To find the mouse's displacement, we need to calculate the straight-line distance between the starting point and the endpoint.
We can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the mouse first scurries 41 cm south, which we can consider as the vertical side of a right triangle. Then it takes a 90-degree turn and goes 64 cm west, which we can consider as the horizontal side of the triangle.
Let's denote the vertical distance as "a" and the horizontal distance as "b". Using the Pythagorean theorem, we have:
a^2 + b^2 = c^2
where "c" represents the hypotenuse, which is the displacement we're looking for.
Substituting the given values, we have:
41^2 + 64^2 = c^2
1681 + 4096 = c^2
5777 = c^2
By taking the square root of both sides, we find that:
c = √5777
Approximating the square root, we find that c is approximately 76.04 cm.
Therefore, the mouse's displacement from its starting point to the cheese is approximately 76.04 cm.