In this question use g=9.8g = 9.8g=9.8 m s−2^{-2}−2.
A ball is projected with speed U U\,U m s−1^{-1}−1 from a point OOO, which is 20 m above horizontal ground. The ball is projected at an angle of 45° 45°\,45° above the horizontal.
The point A A\,A is on the ground vertically below OOO. The ball hits the ground at the point BBB, where AB=80AB = 80AB=80 m. The motion of the ball is modelled as that of a particle moving freely under gravity, with air resistance negligible.
Find the value of UUU.
Find the greatest height of the ball above the ground.
A refined model includes the effect of air resistance. State how the value of U U\,U needed to reach B B\,B would compare with your answer to part (a).
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.