Mathematics 9709 · AS & A Level · Representation of data

Representation of data — practice question

The point $O$ lies $8\,\text{m}$ above a horizontal plane. A particle $P$ is projected from $O$. Once projected, the horizontal displacement of $P$ from $O$ is $x\,\text{m}$ and its vertically upward displacement from $O$ is $y\,\text{m}$. The path of $P$ is given by $y = 2x - x^2$.
(i)[2]

Find the value of $x$ for the point at which $P$ hits the plane.

(ii)[3]

Find the angle of projection and the speed with which $P$ is projected.

(iii)[2]

Calculate the speed of $P$ just before it hits the plane.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Put $y=-8$ into the equation and then try to solve $-8=2x-x^2$” …

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