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.
91 exam-style questions on OCR (MEI) A Level Maths 3.3 Projectiles (A-level only), covering 3.3.1 Model motion under gravity using vectors (A-level only), 3.3.2 Position, velocity, range and maximum height (A-level only), 3.3.3 Find the initial velocity of a projectile (A-level only), 3.3.4 Equation of the trajectory (A-level only), and 3.3.5 Solve simple projectile problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.