Question

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? Sketch it.

Answer 1

Answer:

9.61 m

Explanation:

d1 = 8 m north

d2 = 1 m north west

d3 = 1 m vertically down

Write the displacements in vector form

$\overrightarrow{d_{1}}=8\widehat{j}m$

$\overrightarrow{d_{2}}=1 \left ( -Cos45\widehat{i}+Sin45\widehat{j} \right )m$

$\overrightarrow{d_{2}}=\left ( -0.707\widehat{i}+0.707\widehat{j} \right )m$

$\overrightarrow{d_{3}}=-1\widehat{k}m$

The resultant displacement is given by

$\overrightarrow{d}=\overrightarrow{d_{1}}+ \overrightarrow{d_{2}} +\overrightarrow{d_{3}}$

$\overrightarrow{d}=-0.707\widehat{i}+ 8.707\widehat{j} - 4\widehat{k}m$

The magnitude of displacement is given by

d =

$\sqrt{\left ( -0.707 \right )^{2}+\left ( 8.707 \right )^{2}+\left ( -4 \right )^{2}}$

d = 9.61 m