Question

A truck travelling due north at $20m/s$ turns west and travels at the same speed. The change in its velocity be

• A. $40m/sS-W$
• B. $20\sqrt{2}m/sS-W$
• C. $40m/sN-W$
• D. $20\sqrt{2}m/sN-W$

Answer 1

The correct option is B $20\sqrt{2}m/sS-W$

Draw a rough sketch of the given problem.

Find the change in velocity of the truck.
From figure
Velocity of truck travelling due north,
${\overrightarrow{v}}_1=20\hat{j}m/s$
Velocity of truck when it turns west,
${\overrightarrow{v}}_2=-20\hat{i}m/s$
So, the change in velocity of the truck is
$\Delta \overrightarrow{v}={\overrightarrow{v}}_2-{\overrightarrow{v}}_1=-20(\overrightarrow{i}+\overrightarrow{j})m/s$
$|\Delta \overrightarrow{v}|=20\sqrt{2}m/s$
Direction,
$\theta ={\tan }^{-1}\left(1\right)={45}^{\circ }i.e.,S-W$
Final Answer: (D)