Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A particle $P$ is fired with speed $35\,\text{m s}^{-1}$ from a point $O$ on a horizontal plane. Throughout the motion that follows, the horizontal and vertically upwards displacements of $P$ from $O$ are $x\,\text{m}$ and $y\,\text{m}$ respectively. The path of $P$ is given by $y = kx - \dfrac{(1 + k^2)x^2}{245}$, where $k$ is a constant. $P$ goes through the points $A(14, a)$ and $B(42, 2a)$, where $a$ is a constant.
(i)[5]
Calculate the two possible values of $k$ and hence show that the larger of the two possible angles of projection is $63.435^\circ$, correct to $3$ decimal places.
(ii)[2]
For the larger angle of projection, calculate the time after projection when $P$ passes through $A$.
(iii)[4]
For the larger angle of projection, calculate the speed and direction of $P$ as it passes through $B$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Sets up the equations $a=14k-0.8(1+k^2)$ and $2a=42k-7.2(1+k^2)$” …