A rabbit trying to escape a fox runs north for 8.0 m, darts northwest for 1.0 m, then drops 1.0 m down a hole into its burrow. What is the magnitude of the net displacement of the rabbit?
A) 8.8 m
B) 8.1 m
C) 66 m
D) 10 m

Question

Quizplus · Accepted Answer

The net displacement is the straight-line distance from the starting point to the ending point. The rabbit runs 8.0 m north, then 1.0 m northwest, which is at a 45-degree angle from north. The horizontal component of the northwest displacement is 1.0 m * cos(45) = 0.71 m. The vertical component of the northwest displacement is 1.0 m * sin(45) = 0.71 m. The total horizontal displacement is 8.0 m + 0.71 m = 8.71 m. The total vertical displacement is 0.71 m - 1.0 m = -0.29 m. The magnitude of the net displacement is the square root of the sum of the squares of the horizontal and vertical displacements: sqrt((8.71 m)^2 + (-0.29 m)^2) = 8.8 m.

A Rabbit Trying to Escape a Fox Runs North for 8.0