Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A small object is launched from point $O$ at the foot of a plane inclined at $45^\circ$ to the horizontal, with speed $24\,\text{m s}^{-1}$. Its projection angle is $15^\circ$ above the line of greatest slope of the plane (see diagram). After $t\,\text{s}$, the object's horizontal displacement from $O$ is $x\,\text{m}$ and its vertically upward displacement from $O$ is $y\,\text{m}$.
(i)[4]
Find $x$ and $y$ as functions of $t$, and hence determine the value of $t$ at the moment when the object strikes the plane.
(ii)[5]
Write the vertical height of the object above the plane as a function of $t$, and hence determine the greatest vertical height above the plane.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “From horizontal motion, $x = (24\cos 60)t$.” …