OCR A Level: Mechanics 2 - Projectile Motion [January 2013 Q7]

A particle is projected with speed $u ~\text{ms}^{-1}$ at an angle of $\theta$ above the horizontal from a point $O$ . At time $t ~\text{s}$ after projection, the horizontal and vertically upwards displacements of the particle from $O$ are $x ~\text{m}$ and $y ~\text{m}$ respectively.

$(\text{i})$ Express $x$ and $y$ in terms of $t$ and $\theta$ and hence obtain the equation of trajectory $\large y= x\tan \theta -\dfrac{gx^2 \text{sec}^2 \theta}{2u^2}$

In a shot put competition, a shot is thrown from a height of $2.1 \text{m}$ above horizontal ground. It has initial velocity of $14 \text{ms}^{-1}$ at an angle of $\theta$ above the horizontal. The shot travels a horizontal distance of $22 \text{m}$ before hitting the ground.

$(\text{ii})$ Show that $12.1 \tan^2 \theta - 22 \tan \theta +10=0$ , hence find $\theta$ .

$(\text{ii})$ Find the time of flight of the shot.

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Input the time of flight to three significant figures.

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There are 4 marks available for part (i), 5 marks for part (ii) and 2 marks for part (iii).

In total, this question is worth 15.3% of all available marks in the paper.

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This is part of the set OCR A Level Problems .