Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A small object is fired horizontally at speed $V\,\text{m s}^{-1}$ from point $O$ above level ground. After $t\,\text{s}$, its horizontal displacement from $O$ is $x\,\text{m}$ and its displacement vertically upwards from $O$ is $y\,\text{m}$.
(i)[3]
Write $x$ and $y$ in terms of $t$ and therefore show that the equation of the object’s path is $y = -\frac{5x^2}{V^2}$.
(ii)[3]
The object goes through the points $(a, -a)$ and $(a^2, -16a)$, where $a$ is a positive constant. Determine the value of $a$.
(iii)[2]
Knowing that the object reaches the ground at the point where $x = 5a$, find the height of $O$ above the ground.
(c(iii))[2]
The object hits the ground at the point where $x = 5a$; determine the height of $O$ above the ground.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Work from the horizontal or the vertical motion, for example $x = Vt$ or $y = -\tfrac12 gt^2$” …