$A$ cricket player can throw a ball with an initial speed of $30 \,m/s$. What is the maximum range the player can throw the ball? Neglect air resistance. [Take $g = 10 \,m/s^2$]

$A$ projectile is given an initial velocity of $\hat{i}+2 \hat{j} \,ms^{-1}$. The Cartesian equation of its path is ($x$ and $y$ are in metres and $g=10 \,ms^{-2}$)

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?

An object is projected in the air with initial velocity $u$ at an angle $\theta$. The projectile motion is such that the horizontal range $R$ is maximum. Another object is projected in the air with a horizontal range half of the range of the first object. The initial velocity remains the same in both cases. The value of the angle of projection,at which the second object is projected,will be $.......$ degrees.

It is possible to project a particle with a given velocity in two possible ways so as to make them pass through a point $P$ at a horizontal distance $r$ from the point of projection. If $t_1$ and $t_2$ are times taken to reach this point in two possible ways,then the product $t_1 t_2$ is proportional to

If the range of a gun which fires a shell with muzzle speed $V$ is $R$,then the angle of elevation of the gun is