Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A particle $P$ is launched from point $O$ on level ground. At time $t\,\text{s}$ after the launch, its horizontal displacement from $O$ is $x\,\text{m}$ and its vertical upward displacement is $y\,\text{m}$. The path of $P$ is given by $y = 3x - 0.05x^2$.
(i)[3]
Determine the angle of projection and the initial speed of $P$.
(ii)[2]
Find the coordinates of $P$ at the moment when $OP$ is inclined at $45^{\circ}$ to the horizontal.
(iii)[4]
At the instant when $P$ is at its maximum height above the ground, calculate that height and the corresponding value of $t$.
(c(iii))[4]
At the instant when $P$ is at its maximum height above the ground, calculate that height and the corresponding value of $t$.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies $\tan \theta = 3$ to get $\theta = 71.6^\circ$” …