Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A particle $P$ is fired from a point $O$ on a horizontal plane with speed $35\,\text{m s}^{-1}$. During its motion, its horizontal displacement from $O$ is $x\,\text{m}$ and its vertical upward displacement from $O$ is $y\,\text{m}$. The path of $P$ is given by $y = kx - \frac{(1 + k^2)x^2}{245}$, 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]
Find the speed and direction of motion of $P$ when it passes through $B$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme.