Mathematics 9709 · AS & A Level · Representation of data

Representation of data — practice question

A particle $P$ is launched with speed $25\,\text{m s}^{-1}$ at an angle of $30^\circ$ above the horizontal from point $O$ on horizontal ground. After $t\,\text{s}$, the horizontal displacement of $P$ from $O$ is $x\,\text{m}$ and the vertical upward displacement is $y\,\text{m}$.
(i)[4]

Write $x$ and $y$ in terms of $t$ and hence deduce that the trajectory equation of $P$ is $y = \frac{x}{\sqrt{3}} - \frac{4x^2}{375}$.

(ii)[3]

Determine the horizontal separation between the two points at which $P$ is $5\,\text{m}$ above the ground.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Horizontal component: $x = (25\cos30)t$

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