AQA M1 — Question 5

Exam BoardAQA
ModuleM1 (Mechanics 1)
TopicProjectiles

5 A golf ball is projected from a point \(O\) with initial velocity \(V\) at an angle \(\alpha\) to the horizontal. The ball first hits the ground at a point \(A\) which is at the same horizontal level as \(O\), as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{6151e6ab-30af-4d1c-ab4a-e7dbad170cbf-005_227_602_484_735} It is given that \(V \cos \alpha = 6 u\) and \(V \sin \alpha = 2.5 u\).
  1. Show that the time taken for the ball to travel from \(O\) to \(A\) is \(\frac { 5 u } { g }\).
  2. Find, in terms of \(g\) and \(u\), the distance \(O A\).
  3. Find \(V\), in terms of \(u\).
  4. State, in terms of \(u\), the least speed of the ball during its flight from \(O\) to \(A\).