Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A small ball is projected horizontally at $5\,\text{m s}^{-1}$ from point $O$ on the roof of a building. After $t\,\text{s}$ have passed since it was projected, its horizontal displacement from $O$ is $x\,\text{m}$ and its vertical displacement downwards from $O$ is $y\,\text{m}$.
(i)[3]
Write $x$ and $y$ as functions of $t$, and hence show that the trajectory equation of the ball is $y = 0.2x^2$.
(ii)[6]
The ball lands on the horizontal ground around the building at point $A$. Since $OA = 18\,\text{m}$, calculate the value of $x$ at $A$, together with the speed of the ball immediately before it reaches the ground at $A$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct equation of motion is $y = gt^2/2$.” …