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

Classical Mechanics Level pending

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.

Input the time of flight to three significant figures.

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