A bird is flying towards north with a velocity 40km/h and a train is moving with a velocity 40km/h towards east. What is the velocity of the bird noted by a man in the train?

To find the relative velocity of bird w.r.t train, superimpose velocity

$-{\overrightarrow{V}}_T$  on both the objects. Now as a result of it, the train is at rest,

while bird posses two velocities $-{\overrightarrow{V}}_B$  towards N and $-{\overrightarrow{V}}_T$  along west.

Where, $-{\overrightarrow{V}}_B$  = Velocity of bird       

$-{\overrightarrow{V}}_T$  = Velocity of train.

$\left|{\overrightarrow{V}}_{BT}\right|=\sqrt{|{\overrightarrow{V}}_B{|}^2+|{\overrightarrow{-V}}_T{|}^2}$

[By formula, $\therefore \theta ={90}^0$ ]

$=\sqrt{{40}^2+{40}^2}=40\sqrt{2}km/hrNorth-West$