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.
Practise AQA A Level Maths 1.6 C: Coordinate geometry in the (x, y) plane with exam-style questions for A Level Maths. 110 questions covering 1.6.1 Equation of a straight line, 1.6.2 Coordinate geometry of the circle, 1.6.3 Parametric equations of curves (A-level only), and 1.6.4 Parametric equations in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
