Solution

Engineering Mechanics (Dynamics)

Chapter 12

Exercise 223

(a)

(b)

$$\begin{array}{rl}{\vec{v}}_{A/B}^{}& \\ & ={\vec{v}}_A-{\vec{v}}_B\\ & =-5\hat{i}+8.66\hat{j}-10.61\hat{i}-10.61\hat{j}\\ & =(-15.61\hat{i}-1.95\hat{j})\text{m/s.}\\ & \\ v_{A/B}& =\sqrt{15.61^2+1.95^2}\\ & =15.73\text{m/s.}\end{array}$$

Time needed for boats to be $s = 600$ m apart is:

$$\begin{align*} t &= \frac{s}{v_{A/B}} \\ &= \frac{600}{15.73} \\ &= 38.14 \, \text{s.} \end{align*}$$

Answer

$15.73$ m/s $t = 38.14$ s.