Question

A sail boat sails $2km$ due east, $5km{37}^{\circ }$ south of east and finally an unknown displacement. If the final displacement of the boat from the starting point is $6km$ due east, the third displacement is......... .

Answer 1

Given : $\overrightarrow{S_1}=2\hat{i}$ $\overrightarrow{S_2}=5cos{37}^o\hat{i}-5sin{37}^o\hat{j}$

Net displacement of the sail boat $\overrightarrow{S}=6\hat{i}$

Let the third displacement be $\overrightarrow{S_3}$.

$\therefore$ $6\hat{i}=2\hat{i}+(5cos{37}^o\hat{i}-5sin{37}^o\hat{j})+\overrightarrow{S_3}$

OR $6\hat{i}=2\hat{i}+(4\hat{i}-3\hat{j})+\overrightarrow{S_3}$ $⟹$ $\overrightarrow{S_3}=3\hat{j}$