Question

A boat is travelling with a speed of $27km/h$ due east. An observer is situated at $30m$ south of the line of travel. The angular velocity of boat relative to the observer in the position shown is $\left(\frac{2}{X}\right)$ $rad/s$. Find the value of $X$.

• A. $8$
• B. $9$
• C. $7$
• D. $6$

Answer 1

The correct option is A $8$

Velocity of the boat relative to the observer is $27\hat{i}$ kmph
Angular velocity of the boat with respect to the observer $=\frac{v}{r}=\frac{27\times \frac{5}{18}}{30}=\frac{1}{4}=\frac{2}{8}$ rad /sec
Hence $X=8$