Question

A bird is flying with a speed of $40$ km/hr in the north direction. A train is moving with a speed of $40$ km/hr in the west distance. A passenger sitting in the train will see the bird moving with velocity

• A. $40$ km/hr in N-E direction
• B. $40\sqrt{2}$ km/hr in N-E direction
• C. $40$ km/hr in N-W direction
• D. $40\sqrt{2}$ km/hr in N-W direction

Answer 1

Answer: (B)

$40\sqrt{2}$ km/hr in N-E direction

${\overrightarrow{v}}_{bt}={\overrightarrow{v}}_b-{\overrightarrow{v}}_T$
$\Rightarrow {\overrightarrow{v}}_{bT}=40\hat{j}+40\hat{i}$
$\Rightarrow |{\overrightarrow{v}}_{bT}|=40\sqrt{2}km/h$

$tan\theta =\frac{40}{40}=1\Rightarrow \theta ={45}^{\circ }$
Direction $\Rightarrow N-E$