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).

• A. $40$ km/hr, at an angle $tan^{-1} \left(\frac{3}{5}\right)$ east of south
• B. 50 km/hr, at an angle $tan^{-1} \left(\frac{3}{5}\right)$ east of south
• C. $40$ km/hr, at an angle $tan^{-1} \left(\frac{3}{4}\right)$ east of south
• D. $50$ km/hr, at an angle $tan^{-1} \left(\frac{3}{4}\right)$ east of south

Answer 1

Answer: (D)

$\vec{v}_{A} =40\hat{j}, \vec{v}_{B}=30\hat{i}$
$\vec{v}_{B/A}=\vec{v}_{B}-\vec{v}_{A}=30\hat{i}-40\hat{j}$
$\left|\vec{v}_{B/A}\right|=\sqrt{30^{2}+40^{2}}=50 \,Km /h$