Question

A body is moving with an initial velocity of $10 \sqrt{2} m \cdot s ^{-1}$ in the north-east direction. If it is subjected to an acceleration of $2\, m \cdot s ^{-2}$ directed towards the south, the velocity of the body after $5\, s$ is_____

• A. $10\, m \cdot s ^{-1}$, towards east
• B. $10\, m \cdot s ^{-1}$, towards north
• C. $10\, m \cdot s ^{-1}$, towards south
• D. $10\, m \cdot s ^{-1}$, towards north-east

Answer 1

Answer: (A)

The given situation is shown in the following figure

Initial velocity of body,
$u=10 \sqrt{2} \cos 45^{\circ} \hat{i}+10 \sqrt{2} \cos 45^{\circ} \hat{j}$
$=10 \hat{i}+10 \hat{j}=10(\hat{i}+\hat{j})$
Acceleration applied on body in south direction,
$a_{S}=2(-\hat{j})=-2 \hat{j}$
$\therefore $ Velocity of body after $5 s$ is given as
$v=u +a_{S} t=10(\hat{i}+\hat{j})+(-2 \hat{j}) \times 5$
$=10 \hat{i}+10 \hat{j}-10 \hat{j}=10 \hat{i}$
Hence, body will move towards east with the velocity $10\, ms ^{-1}$.