Question

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? (1 point) the mouse’s displacement is 5 m northwest and it ran 9 m. the mouse’s displacement is 9 m and it ran 5 m. the mouse’s displacement is 5 m southwest and it ran 9 m. the mouse’s displacement is 0 m and it ran 9 m.

Explanation:

Step1: Calculate the total distance

The mouse runs 5 m north, then 1 m south, and then 3 m west. The total distance \(d\) is the sum of these lengths. So \(d = 5+1 + 3=9\) m.

Step2: Calculate the displacement in the north - south direction

The mouse moves 5 m north and 1 m south. The net displacement in the north - south direction \(y=5 - 1=4\) m north.

Step3: Calculate the displacement in the west - east direction

The mouse moves 3 m west, so \(x = 3\) m west.

Step4: Calculate the magnitude of the displacement

Using the Pythagorean theorem for the right - triangle formed by the north - south and west - east displacements. The magnitude of the displacement \(D=\sqrt{x^{2}+y^{2}}=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5\) m. The direction is northwest.

Answer:

The mouse’s displacement is 5 m northwest and it ran 9 m.