The velocity at the maximum height of a projectile is half of its initial velocity $u$. Its range on the horizontal plane is

$A$ boy can throw a stone up to a maximum height of $10 \ m$. The maximum horizontal distance that the boy can throw the same stone up to will be .......... $m$.

$A$ body is projected with a velocity $(\hat{i} + 2\hat{j}) \text{ ms}^{-1}$,where $\hat{i}$ is along the horizontal and $\hat{j}$ is vertically upward. Then the equation of its trajectory is $(g = 10 \text{ ms}^{-2})$.

$A$ particle is projected from the ground with an initial speed of $v$ at an angle of projection $\theta$. The average velocity of the particle between its time of projection and the time it reaches the highest point of its trajectory is

$A$ body is thrown at an angle of $30^{\circ}$ to the horizontal with a velocity of $30\; m/s$. After $1\; s$,its velocity will be (in $m/s$) $\left(g=10\; m/s^{2}\right)$

$A$ particle is projected at $60^{\circ}$ to the horizontal with a kinetic energy $K$. The kinetic energy at the highest point is