A particle is projected with speed $10 \mathrm{m s}^{-1}$  from a flat horizontal surface. Find, with proof, the angle from which it should be projected to maximise the distance travelled before it hits the surface. Does this angle depend on the speed of projection?
The particle is now projected with speed $10 \mathrm{m s}^{-1}$  from a height of $2$ metres.