Question

A car going due North at $20\sqrt{2}m/s$ turns right through an angle of ${90}^{\circ }$ without changing speed. The change in velocity of car is

• A. $20m/s$in South-East direction
• B. $20m/s$ in North−West direction
• C. $20m/s$North-East direction
• D. $20\sqrt{2}m/s$ in South-East direction

Answer 1

The correct option is A $20m/s$in South-East direction

Draw a labelled diagram.

Find change in the velocity.
Initial velocity, ${\overrightarrow{v}}_i=10\sqrt{2}\hat{j}$
Final velocity, ${\overrightarrow{v}}_f=10\sqrt{2}\hat{i}$
$\therefore$ The change in velocity is,
$\Delta \overrightarrow{v}={\overrightarrow{v}}_f-{\overrightarrow{v}}_i=10\sqrt{2}\hat{i}-10\sqrt{2}\hat{j}$

$\therefore$ Magnitude of change in velocity,
$|\Delta \overrightarrow{v}|=\sqrt{(10\sqrt{2}{)}^2+(10\sqrt{2}{)}^2}=\sqrt{400}$
$|\Delta \overrightarrow{v}|=20m/s$ in South-East direction.
Final Answer: (A)