Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A small object is launched with speed $24\,\text{m s}^{-1}$ from point $O$ at the base of a plane inclined at $45^\circ$ to the horizontal. The object is projected at an angle of $15^\circ$ above a line of greatest slope on the plane (see diagram). After $t$ s from projection, the object's horizontal displacement from $O$ is $x$ m and its vertically upward displacement from $O$ is $y$ m.
(i)[4]
Express $x$ and $y$ in terms of $t$, and hence find the value of $t$ at the moment when the object strikes the plane.
(ii)[5]
Express the vertical height of the object above the plane as a function of $t$ and hence find the greatest vertical height of the object above the plane.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme.