Question

A car \(A\) moves due north at a speed of \(40~km/hr\), while another car 𝐵 moves due east at a speed of \(30~km/hr\). Find the velocity of car \(B\) relative to car \(A\) (both in magnitude and direction).

Answer 1

Given, Velocity of car \(B=30\hat{i}~km/hr\)
Velocity of car \(A=40\hat{j}~km/hr\)
\(\vec{v}_{BA}=\vec{v}_B-\vec{v}_A=30\hat{i}-40\hat{j}\)
\(\left | \vec{v}_{BA} \right |=\sqrt{30^2+(-40)^2}\)
\(=50\dfrac{km}{h}\)
Direction of \(\vec{v}_{BA}\):
\(\tan\phi =\dfrac{v_B}{v_A}=-\dfrac{3}{4}\)
\(\phi =\tan^-1\left ( \dfrac{-3}{4} \right )\)
\(50~km/hr\), at an angle \(\tan^-1\left ( \dfrac{3}{4} \right )\) east of south
Final Answer: (d)