a mouse runs 5 m north across the floor before hearing a cat. then it runs back south along the same path…
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.
Answer
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.