A cannon on a level plain is aimed at an angle $\mathrm{\alpha }$ above the horizontal and a shell is fired with a muzzle velocity v_o towards a vertical cliff a distance R away. Then the height from the bottom at which the shell strikes the side walls of the cliff is

• A

  $\mathrm{R} \sin \mathrm{\alpha }-\frac{1}{2}\frac{{\mathrm{gR}}^2}{{\mathrm{v}}_0^2{\sin }^2\mathrm{\alpha }}$

• B

  $\mathrm{R} \cos \mathrm{\alpha }-\frac{1}{2}\frac{{\mathrm{gR}}^2}{{\mathrm{v}}_0^2{\cos }^2\mathrm{\alpha }}$

• C

  $\mathrm{R} \tan \mathrm{\alpha }-\frac{1}{2}\frac{{\mathrm{gR}}^2}{{\mathrm{v}}_0^2{\cos }^2\mathrm{\alpha }}$

• D

  $\mathrm{R} \tan \mathrm{\alpha }-\frac{1}{2}\frac{{\mathrm{gR}}^2}{{\mathrm{v}}_0^2{\sin }^2\mathrm{\alpha }}$