Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A particle $P$ is launched from point $O$ with initial speed $10\,\text{m s}^{-1}$ at $45^\circ$ above the horizontal. $P$ later passes through point $A$, which is at an angle of elevation of $30^\circ$ from $O$ (see diagram). After $t$ s from projection, the horizontal displacement and the vertically upward displacement of $P$ from $O$ are $x$ m and $y$ m respectively.
(i)[3]
Express $x$ and $y$ in terms of $t$, and hence derive the equation for the trajectory of $P$.
(ii)[3]
Calculate the value of $x$ at the instant when $P$ is at $A$.
(iii)[4]
Find the angle made by the trajectory with the horizontal when $P$ is at $A$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies $x=(10\cos45^\circ)t$ and $y=(10\sin45^\circ)t-gt^2/2$” …