$A$ projectile fired with initial velocity $u$ at an angle $\theta$ has a range $R$. If the initial velocity is doubled at the same angle of projection,then the new range will be:

$A$ small object is thrown at an angle $45^{\circ}$ to the horizontal with an initial velocity $v_0$. The velocity is averaged for the first $\sqrt{2} \,s$ and the magnitude of the average velocity comes out to be the same as that of the initial velocity, i.e.,$|v_0|$. The magnitude $|v_0|$ will be (take $g=10 \,m/s^2$):

$A$ stone is projected at an angle $\theta$ with velocity $u$. If it executes nearly a circular motion at its maximum point for a short time,the radius of the circular path will be ($g=$ acceleration due to gravity).

If a body is projected with an angle $\theta$ to the horizontal, then

$A$ ball thrown by one player reaches another player in $2 \text{ s}$. The maximum height attained by the ball above the point of projection will be $.... \text{ m}$.

$A$ bullet is fired with a speed of $1000 \, m/s$ in order to hit a target $100 \, m$ away. If $g = 10 \, m/s^2$,the gun should be aimed: