(i) State the principle of dimensional homogeneity of physical equations.
(ii) The range R of a projectile projected with an initial speed u at an angle θ to the horizontal is written by a student as
R=gusin2θ.
Examine whether this expression is dimensionally consistent.
(iii) Another student writes the alternative expression
R=g2u2sin2θ.
Using dimensional considerations only, explain why this expression cannot be correct.