Question

A ship is steaming towards east with speed of $8m/s$. A women runs across the deck at a speed of $6{ms}^{-1}$ towards north. What is the velocity of the women relative to the sea?

Answer 1

Relative velocity of women w.r.t water=velocity of woman w.r.t ship - velocity of ship w.r.t water

$\overrightarrow{v_w}-\overrightarrow{v_s}=\overrightarrow{v_w}+(-\overrightarrow{v_s})$

The relative velocity of woman w.r.t water is along the resultant of $\overrightarrow{v_w}$ and $-\overrightarrow{v_s}$

Its magnitude is $\sqrt{v_w^2+v_s^2}=\sqrt{6^2+8^2}$

$=10m/s$