A ball is kicked from a point O O\,O on level horizontal ground with velocity U ms−1U \text{ ms}^{-1}U ms−1 at an angle θ \theta\,θ to the horizontal. At horizontal distance x x\,x from OOO, the height of the ball is yyy.
Show that the equation of the path of the ball is
y=xtanθ−gx22U2cos2θ y = x \tan \theta - \frac{g x^2}{2 U^2 \cos^2 \theta} y=xtanθ−2U2cos2θgx2Given that θ=60∘\theta = 60^\circθ=60∘ and that when x=10x = 10x=10, y=4y = 4y=4, find the speed of the ball at the point where x=10x = 10x=10 and y=4y = 4y=4.
260 exam-style questions on OCR A Level Maths 3.2 Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Displacement-time and velocity-time graphs, 3.2.4 Constant acceleration formulae, 3.2.5 Constant acceleration in two dimensions (A-level only), 3.2.6 Non-uniform acceleration in one dimension (A-level only), 3.2.7 Non-uniform acceleration in two dimensions (A-level only), 3.2.8 Motion under gravity using vectors (A-level only), and 3.2.9 Projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.