# The gun o'er the hill

**Classical Mechanics**Level 3

A gun is located at the top of a hill of height \( h \) above the horizontal plane.It fires two shells with the same velocity \(u\) at angles \(\alpha\) and \(\beta\) with the horizontal.If the shells strike the horizontal ground at the same place then the value of \(h\) can be expressed as \[h=\frac{a u^{2} (1-\tan\alpha \tan\beta)}{g (\tan\alpha+\tan\beta)}\] where \(a\) is an integer whose value is: