A stone is thrown from the origin O O\,O with initial velocity W ms−1W \text{ ms}^{-1}W ms−1 at an angle β \beta\,β to the horizontal. At time t t\,t seconds, its horizontal and vertical displacements are x x\,x and y y\,y respectively.
Prove that
y=xtanβ−gx22W2cos2β y = x \tan \beta - \frac{g x^2}{2 W^2 \cos^2 \beta} y=xtanβ−2W2cos2βgx2Given that tanβ=34\displaystyle \tan \beta = \frac{3}{4}tanβ=43 and that when x=4x = 4x=4, y=1y = 1y=1, find the speed of the stone at the point where x=4x = 4x=4.
