(i)[4]
Express $x$ and $y$ in terms of $t$ and hence find the equation of the trajectory of $P$.
(ii)[3]
$P$ is at the same height above the ground at two points which are a horizontal distance apart of $15\,\text{m}$. Calculate this height.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A particle $P$ is fired from a point $O$ on horizontal ground with initial speed $20\,\text{m s}^{-1}$ at an angle of projection $30^\circ$. After $t$ s, the horizontal displacement of $P$ from $O$ is $x$ m and the vertical displacement upwards from $O$ is $y$ m.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “From horizontal motion, use $x = 20 \cos 30^\circ \, t = 10 \sqrt{3}\, t$” …
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