Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A particle is fired from a point $O$ on level ground. The initial speed is $20\,\text{m s}^{-1}$, and it is directed upwards at an angle $\theta$ to the horizontal. The particle goes through the point that is $7\,\text{m}$ above the ground and $16\,\text{m}$ horizontally from $O$, and lands on the ground at $A$.
(i)[4]
From the trajectory equation and the identity $\sec^2\theta = 1 + \tan^2\theta$, demonstrate that the possible values of $\tan \theta$ are $\frac{3}{4}$ and $\frac{17}{4}$.
(ii)[3]
Determine the distance $OA$ for each of the two admissible values of $\tan \theta$.
(iii)[2]
On the same diagram, sketch the two possible trajectories.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme.