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.
178 exam-style questions on OCR (MEI) A Level Maths 1.5 Coordinate Geometry, covering 1.5.1 Equation of a straight line y = mx + c, 1.5.2 Gradients of parallel and perpendicular lines, 1.5.3 Distance between two points, 1.5.4 Midpoint of a line segment, 1.5.5 Form the equation of a straight line, 1.5.6 Draw a line given its equation, 1.5.7 Point of intersection of two lines, 1.5.8 Straight line models, 1.5.9 Intersection of a line and a curve, 1.5.10 Intersection of a line and a circle, 1.5.11 Equation of a circle, 1.5.12 Circle properties, 1.5.13 Parameter and parametric equations (A-level only), 1.5.14 Convert between cartesian and parametric forms (A-level only), 1.5.15 Equation of a circle in parametric form (A-level only), 1.5.16 Gradient of a parametric curve (A-level only), 1.5.17 Parametric equations in modelling (A-level only), and 1.5 Coordinate Geometry. Each one has a worked solution and a mark scheme showing where the marks go.