Question

Two boats leave shore. One moves due north at 10 m/s speed, and the other at ${37}^o$ North of East at 10 m/s. The speed of one boat with respect to another is ($\sqrt{5}=2.236$)
Write the answer until two digits after the decimal point.

Answer 1

Take north as y axis and east as x axis.
${\overrightarrow{V}}_A=10\hat{j},{\overrightarrow{V}}_B=10\cos 37\hat{i}+10\sin 37\hat{j}{\overrightarrow{V}}_B=8\hat{i}+6\hat{j}\Rightarrow {\overrightarrow{V}}_{AB}={\overrightarrow{V}}_A-{\overrightarrow{V}}_B=-8\hat{i}+4\hat{j}|{\overrightarrow{V}}_{AB}|=\sqrt{8^2+4^2}=\sqrt{64+16}=\sqrt{80}=8.94$