Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A light ball $B$ is launched from point $O$ with speed $15\,\mathrm{m\,s^{-1}}$ at $41^\circ$ above the horizontal. Point $O$ is $1.6\,\mathrm{m}$ above level ground. After $t\,\mathrm{s}$ from launch, the horizontal displacement of $B$ from $O$ is $x\,\mathrm{m}$ and its vertical upward displacement from $O$ is $y\,\mathrm{m}$. A vertical fence stands $1.5\,\mathrm{m}$ from $O$ and is perpendicular to the plane of motion of $B$. The ball just clears the fence and then lands on the ground at $A$.
(i)[4]
Write $x$ and $y$ in terms of $t$ and so show that the trajectory of $B$ is $y = 0.869x - 0.0390x^2$, with the coefficients accurate to $3$ significant figures.
(ii)[5]
Calculate the height of the fence, and the distance from the fence to $A$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Equation of motion $x = (15\cos 41)t$” …