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A body is thrown at angle $30^{\circ}$ to the horizontal with the velocity of $30\; m / s$. After $1\;sec$, its velocity will be (in $m/s$) $\left(g=10\; m / s ^{2}\right)$
$10\sqrt 7 $
$700\sqrt {10} $
$100\sqrt 7 $
$\sqrt {40} $
Solution
Horizontal component of velocity along $x$-axis after $1 s$ is
$v _{ x }= u _{ x }+ gt$
$v _{ x }= u \cos \theta+0 \times 1$
$v _{ x }=30 \cos 30^{\circ}$
$v _{ x }=15\sqrt3\; m / s$
Vertical component of the velocity along $y$-axis after $1 s$ is
$v _{ y }= u _{ y }- gt$
$v _{ y }=30 \sin 30^{\circ}-10 \times 1$
$v _{ y }=15-10$
$v _{ y }=5 m / s$
Velocity of a body after 1 s is
$\overrightarrow{ v }= v _{ x } \hat{ i }+ v _{ y } \hat{ j }$
$\overrightarrow{ v }=15\sqrt3 \hat{ i }+5 \hat{ j }$
Magnitude, $v =|\overrightarrow{ v }|=\sqrt{(15\sqrt3)^{2}+(5)^{2}}$
$v =\sqrt{700}$
$v =10 \sqrt{7}\; m / s$
