OCR M2 2012 January — Question 7

Exam BoardOCR
ModuleM2 (Mechanics 2)
Year2012
SessionJanuary
TopicProjectiles

7 A particle \(P\) is projected horizontally with speed \(15 \mathrm {~ms} ^ { - 1 }\) from the top of a vertical cliff. At the same instant a particle \(Q\) is projected from the bottom of the cliff, with speed \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(\theta ^ { \circ }\) above the horizontal. \(P\) and \(Q\) move in the same vertical plane. The height of the cliff is 60 m and the ground at the bottom of the cliff is horizontal.
  1. Given that the particles hit the ground simultaneously, find the value of \(\theta\) and find also the distance between the points of impact with the ground.
  2. Given instead that the particles collide, find the value of \(\theta\), and determine whether \(Q\) is rising or falling immediately before this collision.