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1.3 Coordinate Geometry in the x-y Plane

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Question 65

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.

a.

Find a Cartesian equation for the path of the stone, in the form y=f(x)y = f(x)y=f(x).

[3]
b.

Find the horizontal distance travelled by the stone before it hits the sea, giving your answer to three significant figures.

[3]
c.

State one limitation of this model.

[1]
Markscheme

1.3 Coordinate Geometry in the x-y Plane Questions

  1. A Level
  2. /Maths
  3. /1.3 Coordinate Geometry in the x-y Plane

143 exam-style questions on OCR A Level Maths 1.3 Coordinate Geometry in the x-y Plane, covering 1.3.1 Straight lines, 1.3.2 Parallel and perpendicular lines, 1.3.3 Straight line models, 1.3.4 Coordinate geometry of a circle, 1.3.5 Centre and radius by completing the square, 1.3.6 Circle properties, 1.3.7 Parametric equations of curves (A-level only), 1.3.8 Parametric equations in context (A-level only), and 1.3 Coordinate Geometry in the x-y Plane. Each one has a worked solution and a mark scheme showing where the marks go.

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