(i)[4]
Write $x$ and $y$ in terms of $t$ and therefore prove that the path equation of $P$ is $y = x - 0.016x^2$.
(ii)[2]
Find the horizontal separation between the two positions at which $P$ is $2.4\text{ m}$ above the ground.
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 $45^\circ$ above the horizontal. After $t$ s, its horizontal displacement from $O$ is $x\text{ m}$ and its vertically upward displacement from $O$ is $y\text{ m}$.