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.

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

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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.

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This is part of the set OCR A Level Problems .