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 an angle of $45^\circ$ above the horizontal. $P$ later passes through point $A$, which is at an angle of elevation of $30^\circ$ from $O$ (see diagram). After time $t$ from projection, the horizontal displacement of $P$ from $O$ is $x$ and the upward vertical displacement is $y$ m respectively.
(i)[3]
State expressions for $x$ and $y$ in terms of $t$, and hence determine the equation of the trajectory of $P$.
(ii)[3]
Calculate the value of $x$ when $P$ is at $A$.
(iii)[4]
Find the angle the trajectory makes 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: “Employs parametric equations $x=(10\cos45^\circ)t$, $y=(10\sin45^\circ)t-gt^2/2$” …