A cannon ball has a range R on a horizontal plane. If h and h' are the greatest heights in the two paths for which this is possible, then

The range is same for angles α and π2−α.The range R for α is given byR=2u2sin⁡αcos⁡αg      ….(1)Maximum height, h=u2sin2⁡α2g … (2)The range and height corresponding to angle π2-α areR=2u2sin⁡π2−αcos⁡π2−αgand   h′=u2sin2⁡π2−α2g=u2cos2⁡α2gNow   h×h′=u4sin2⁡α×cos2⁡α4g2hh′=u2sin⁡αcos⁡α2g=R4∴ R=4hh′