2
\includegraphics[max width=\textwidth, alt={}, center]{cbe25a5a-0ca7-4e1b-b5b1-141a49186944-03_359_931_251_255} A particle is projected with speed V from a point O on horizontal ground. The angle of projection is \(\theta\) above the horizontal. The particle passes, in succession, through two points A and B , each at a height h above the ground and a distance d apart, as shown in the diagram. You are given that \(d ^ { 2 } = \frac { v ^ { \alpha } \sin ^ { 2 } 2 \theta } { g ^ { \beta } } - \frac { 8 h v ^ { 2 } \cos ^ { 2 } \theta } { g }\). Use dimensional analysis to find \(\alpha\) and \(\beta\).