$A$ body is projected horizontally from the top of a tower of height $180 \ m$ with a velocity of $20 \ ms^{-1}$. If acceleration due to gravity is $10 \ ms^{-2}$,then match the following:
List-$I$ (Kinematic Variable)List-$II$ (Value)
$A$. Velocity of the body after $1 \ s$ (in $ms^{-1}$)$I$. $5$
$B$. Horizontal displacement of the body after $1 \ s$ (in $m$)$II$. $20$
$C$. Vertical displacement of the body after $1 \ s$ (in $m$)$III$. $10$
$D$. Vertical velocity of the body after $1 \ s$ (in $ms^{-1}$)$IV$. $22.4$

The correct answer is

  • A
    $A-IV, B-II, C-III, D-I$
  • B
    $A-I, B-II, C-III, D-IV$
  • C
    $A-IV, B-II, C-I, D-III$
  • D
    $A-II, B-IV, C-I, D-III$

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$A$ body is projected from the top of a tower with a velocity $\overrightarrow{u} = 3 \hat{i} + 4 \hat{j} + 5 \hat{k} \text{ m/s}$, where $\hat{i}, \hat{j},$ and $\hat{k}$ are unit vectors along east, north, and vertically upwards, respectively. If the height of the tower is $30 \text{ m}$, find the horizontal range of the body on the ground. (Take $g = 10 \text{ m/s}^2$) (in $\text{ m}$)

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