A stone is projected from the origin O O\,O with velocity U ms−1U \text{ ms}^{-1}U ms−1 at an angle α \alpha\,α to the horizontal. The stone's coordinates (x,y)(x, y)(x,y) at time t t\,t are relative to OOO.
Show that
y=xtanα−gx22U2cos2α y = x \tan \alpha - \frac{g x^2}{2 U^2 \cos^2 \alpha} y=xtanα−2U2cos2αgx2Given that α=30∘\alpha = 30^\circα=30∘ and that when x=12x = 12x=12, y=3y = 3y=3, find the speed of the stone at the point where x=12x = 12x=12 and y=3y = 3y=3.