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 speed $25\,\text{m s}^{-1}$ at an angle of $30^\circ$ above the horizontal. After $t\,\text{s}$, its horizontal displacement from $O$ is $x\,\text{m}$ and its vertical displacement upwards from $O$ is $y\,\text{m}$, respectively.
(i)[4]
Express $x$ and $y$ as functions of $t$ and hence show that the trajectory equation for $P$ is $y = \frac{x}{\sqrt{3}} - \frac{4x^2}{375}$.
(ii)[3]
Find the horizontal distance between the two points where $P$ 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: “For horizontal motion, $x = (25\cos30)t$” …