A cannon on a level plain is aimed at an angle α above the horizontal and a shell is fired with a muzzle velocity v0 towards a vertical cliff at a distance R away. Then the height from the bottom at which the shell strikes the side walls of the cliff is
R tan α−gR22v20cos2α
The time taken to move a horizontal distance R is t=Rv0 cos α.
Therefore, the vertical distance moved in this time is given by
h=v0 sin α t−12gt2=v0 sin α×Rv0 cos α−12g(Rv0 cos α)2=R tan α−gR22v20 cos2 α
Hence, the correct choice is (c).