OCR M2 2011 June — Question 5

Exam BoardOCR
ModuleM2 (Mechanics 2)
Year2011
SessionJune
TopicProjectiles

5 A particle is projected with speed \(7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of elevation of \(30 ^ { \circ }\) from a point \(O\) and moves freely under gravity. The horizontal and vertically upwards displacements of the particle from \(O\) at any subsequent time \(t \mathrm {~s}\) are \(x \mathrm {~m}\) and \(y \mathrm {~m}\) respectively.
  1. Express \(x\) and \(y\) in terms of \(t\) and hence find the equation of the trajectory of the particle.
  2. Calculate the values of \(x\) when \(y = 0.6\).
  3. Find the direction of motion of the particle when \(y = 0.6\) and the particle is rising.