If R and H are the horizontal range and maximum heights attained by a projectile, then its speed of projection is

We know that Range of a particle us given by, R= u^2sin2(x)/g........ (1) and H=u^2sin>(x)/2g......... (2)Adding (1) & (2)u^2[(2sin^2(x) + sin2(x) /2g] = R + Hu[{2sin(x)(usin(x) + ucos(x))}/2g] = R+H(2usin(x).u)/2g = R+H....... (3)FROM (2) Sin(x) = (2gH)^1/2/u.... (4)putting (4) in (3), we get [u(2gH)^1/2]/g = R+HTHUS we get u =(R+H) g/(2gH)^1/2