Question

A bird is flying towards north with a velocity $40 \,km\,h^{-1}$ and a train is moving with velocity $40 \,km \,h^{-1}$ towards east. What is the velocity of the bird noted by a man in the train?

• A. $40\sqrt{2}\,km\,h^{-1}\,N-E$
• B. $40\sqrt{2}\,km\,h^{-1}\, S-E$
• C. $40\sqrt{2}\,km\,h^{-1}\, N-W$
• D. $40\sqrt{2}\,km\,h^{-1}\, S-W$

Answer 1

Answer: (C)

To find the relative velocity of bird w.r.t. train, superimpose velocity $-\vec{v}_{T}$ on both the objects. Now as a result of it, the train is at rest, while the bird possesses two velocities, $\vec{v}_{B}$ towards north and $-\vec{v}_{T}$ along west

$\left|\vec{v}_{BT}\right|=\sqrt{\left|\vec{v}_{B}\right|^{2} +\left|-\vec{v}_{T}\right|^{2}}$ [By formula, $\theta=90^{\circ}]$
$=\sqrt{40^{2}+40^{2}}=40\sqrt{2}\,km\,h^{-1}$ north-west