CAIE M2 2009 June — Question 5

Exam BoardCAIE
ModuleM2 (Mechanics 2)
Year2009
SessionJune
TopicProjectiles

5 A small stone is projected from a point \(O\) on horizontal ground with speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\theta ^ { \circ }\) above the horizontal. Referred to horizontal and vertically upwards axes through \(O\), the equation of the stone's trajectory is \(y = 0.75 x - 0.02 x ^ { 2 }\), where \(x\) and \(y\) are in metres. Find
  1. the values of \(\theta\) and \(V\),
  2. the distance from \(O\) of the point where the stone hits the ground,
  3. the greatest height reached by the stone.