Four projectiles are fired with the same velocities at angles $25^{\circ}, 40^{\circ}, 55^{\circ}$ and $70^{\circ}$ with the horizontal. The range of the projectile will be largest for the one projected at angle $.......$ . (in $^{\circ}$)

$A$ 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:

$A$. 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 $ms^{-1}$)	$IV$. $22.4$

$A$ projectile is fired with a speed $u$ at an angle $\theta$ with the horizontal. Its speed when its direction of motion makes an angle $\alpha$ with the horizontal is

The trajectory of a projectile in a vertical plane is $y = \alpha x - \beta x^2$,where $\alpha$ and $\beta$ are constants and $x$ and $y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained $H$ are respectively given by:

The path of a projectile in the absence of air drag is shown in the figure by a dotted line. If air resistance is not ignored, then which one of the paths shown in the figure is appropriate for the projectile?

$A$ body is projected from the earth at an angle of $30^{\circ}$ with the horizontal with some initial velocity. If its range is $20 \ m$, the maximum height reached by it is: (in meters)