The velocity of a body at time $ t = 0$ is $10\sqrt 2 \,m/s$ in the north-east direction and it is moving with an acceleration of $ 2 \,m/s^{2}$ directed towards the south. The magnitude and direction of the velocity of the body after $5\, sec$ will be
The velocity of a body at time $ t = 0$ is $10\sqrt 2 \,m/s$ in the north-east direction and it is moving with an acceleration of $ 2 \,m/s^{2}$ directed towards the south. The magnitude and direction of the velocity of the body after $5\, sec$ will be
$10 \,m/s$, towards east
$10 \,m/s$, towards north
$10\, m/s$, towards south
$10\, m/s$, towards north-east
The velocity of a body at time $ t = 0$ is $10\sqrt 2 \,m/s$ in the north-east direction and it is moving with an acceleration of $ 2 \,m/s^{2}$ directed towards the south. The magnitude and direction of the velocity of the body after $5\, sec$ will be
$\overrightarrow v = \overrightarrow u + \overrightarrow a \,t$
$v = \sqrt {{u^2} + {a^2}{t^2} + 2u\,at\cos \theta } $
$v = \sqrt {200 + 100 + 2 \times 10\sqrt 2 \times 10 \times \cos 135} $$ = 10\,m/s$
$\tan \alpha = \frac{{at\sin \theta }}{{u + at\cos \theta }}\frac{{10\sin 135}}{{10\sqrt 2 + 10\cos 135}} = 1$
$\alpha = 45^\circ $
i.e. resultant velocity is $10\, m/s$ towards East.