# 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.

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