CAIE M2 2016 June — Question 3

Exam BoardCAIE
ModuleM2 (Mechanics 2)
Year2016
SessionJune
TopicProjectiles

3 The point \(O\) is 8 m above a horizontal plane. A particle \(P\) is projected from \(O\). After projection, the horizontal and vertically upwards displacements of \(P\) from \(O\) are \(x \mathrm {~m}\) and \(y \mathrm {~m}\) respectively. The equation of the trajectory of \(P\) is $$y = 2 x - x ^ { 2 }$$
  1. Find the value of \(x\) for the point where \(P\) strikes the plane.
  2. Find the angle and speed of projection of \(P\).
  3. Calculate the speed of \(P\) immediately before it strikes the plane.