A crane of efficiency $80 \%$ is used to lift 8000 kg of coal from a mine of depth 108 m . If the time taken by the crane to lift the coal is one hour, then the power of the crane (in kW ) is

(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A train of mass $10^6 \mathrm{~kg}$ is moving at a constant speed of $108 \mathrm{~km} / \mathrm{h}$. If the frictional force acting on it is 0.5 N per 100 kg , then the power of the train is

A body is moving along a straight line under the influence of a constant power source. If the relation between the displacement $(s)$ of the body and time $(t)$ is $s \propto t^x$, then $x=$

A body is projected at an angle of $60^{\circ}$ with the horizontal. If the initial kinetic energy of the body is $X$, then its kinetic energy at the highest point is