A stone is thrown from the edge of a cliff out to sea. Its position t t\,t seconds after being thrown is modelled by
x=12tx = 12tx=12t, y=30−4.9t2y = 30 - 4.9t^2y=30−4.9t2, t≥0 t \geq 0\,t≥0
where x x\,x metres is the horizontal distance from the point of projection and y y\,y metres is the height above sea level.
Find a Cartesian equation for the path of the stone, in the form y=f(x)y = f(x)y=f(x).
Find the horizontal distance travelled by the stone before it hits the sea, giving your answer to three significant figures.
State one limitation of this model.
75 exam-style questions on CCEA A Level Maths 3.2 Co-ordinate geometry in the (x, y) plane (A-level only), covering 3.2.1 Co-ordinate geometry in the (x, y) plane (A-level only) and 3.2.2 Co-ordinate geometry in the (x, y) plane (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.