A football is kicked with speed U ms−1U \text{ ms}^{-1}U ms−1 from a point A A\,A on a roof, 15 m above the level ground. The ball is projected at an angle of 30∘ 30^\circ\,30∘ above the horizontal. The point B B\,B is the greatest height reached by the ball, which is 8 m vertically above AAA.
Find the value of UUU.
Find the horizontal distance travelled by the ball before it hits the ground.
Find the speed of the ball when it hits the ground.
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.