In a sports competition,a javelin is thrown at an angle $45^{\circ}$,which recorded a range of $90 \,m$. The maximum height reached by the javelin is (Neglect air resistance and acceleration due to gravity $g = 10 \,ms^{-2}$)

The maximum height reached by a projectile is $64 \,m$. If the initial velocity is halved, the new maximum height of the projectile is . . . . . . $m$.

$A$ particle is projected from the ground with a kinetic energy $E$ at an angle of $60^{\circ}$ with the horizontal. Its kinetic energy at the highest point of its motion will be

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

For a given velocity,a projectile has the same range $R$ for two angles of projection. If $t_1$ and $t_2$ are the times of flight in the two cases,then:

$A$ stone is projected with kinetic energy $E$,making an angle $\theta$ with the horizontal. When it reaches its highest point,its kinetic energy is