A. Consider a plane OA at an angle y with the horizon as shown below. If a projectile is fired up the inclined surface from the point O with an

initial velocity v making an angle of with the horizon. The projectile follows a parabolic path and strikes the inclined surface at A. \text { 1. Derive an expression for the time of flight of the projectile in terms of } v_{n} \gamma \text { and } \theta \text {. } \text { 2. Derive an expression for the range } \mathrm{R} \text { along the inclined surface in terms of } v, \gamma \text { and } \theta \text {. } 3. Derive an expression for the maximum range Rmax änd the corresponding angle ofprojection. 4. Derive an expression for maximum hight (Hmax) as shown in the figure. 5. Support your answers in (3) and (4) by numerical values.