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 $2m\cdot s^{-2}$ directed towards the south, the velocity of the body after $5s$ is_____

• A. $10m\cdot s^{-1}$, towards east
• B. $10m\cdot s^{-1}$, towards north
• C. $10m\cdot s^{-1}$, towards south
• D. $10m\cdot s^{-1}$, 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 $5s$ 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 $10m{s}^{-1}$.