$A$ projectile is projected with kinetic energy $K$. If it has the maximum possible horizontal range,then its kinetic energy at the highest point will be ......... $K$.

If $R$ and $H$ represent the horizontal range and the maximum height achieved by a projectile,then which of the following relations exists?

Two seconds after projection,a projectile is travelling in a direction inclined at $30^o$ to the horizontal. After one more second,it is travelling horizontally. What is the magnitude and direction of its velocity at the initial point?

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

An object is projected with a velocity of $20 \ m/s$ making an angle of $45^{\circ}$ with the horizontal. The equation for the trajectory is $h = Ax - Bx^2$, where $h$ is the height, $x$ is the horizontal distance, and $A$ and $B$ are constants. The ratio $A:B$ is $(g = 10 \ m/s^2)$.

The velocity of projection of a body is increased by $2 \%$. Other factors remaining unchanged,what will be the percentage change in the maximum height attained? (in $\%$)