OCR A Level: Mechanics 2 - Projectile Motion [January 2012 Q7]

A particle \(P\) is projected horizontally with speed \(15 \text{ms}^{−1}\) from the top of a vertical cliff. At the same instant a particle \(Q\) is projected from the bottom of the cliff, with speed \(25 \text{ms}^{−1}\) at an angle of \(θ°\) above the horizontal. \(P\) and \(Q\) move in the same vertical plane. The height of the cliff is \(60 \text{m}\) and the ground at the bottom of the cliff is horizontal.

\((\text{i})\) Given that the particles hit the ground simultaneously, find the value of \(θ\) and find also the distance between the points of impact with the ground.

\((\text{ii})\) Given instead that the particles collide, find the value of \(θ\), and determine whether \(Q\) is rising or falling immediately before this collision.

Input the value of \(θ\) from part \((\text{ii})\) as your answer, correct to 3 significant figures.

There are 6 marks available for part (i) and 9 marks for part (ii).
In total, this question is worth 20.8% of all available marks in the paper.

This is part of the set OCR A Level Problems.

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