At time ttt hours after a high tide, the height, hhh metres, of the tide and the velocity, vvv knots, of the tidal flow are modelled using the parametric equations
v=9−(3t4−3)2 v = 9 - \left(\frac{3t}{4}-3\right)^2 v=9−(43t−3)2 h=4−3t−43 h = 4 - 3\sqrt[3]{t-4} h=4−33t−4High tides and low tides occur alternately when the velocity of the tidal flow is zero.
A high tide occurs at 4 am.
Use the model to find the height of this high tide.
Find the time of the first low tide after 4 am.
Find the height of this low tide.
Use the model to find the height of the tide when it is flowing with maximum velocity.
Comment on the validity of the model.
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.