The vertical acceleration of a surveillance drone, a(t)a(t)a(t) in m s−2\text{m s}^{-2}m s−2, is modeled by the function H′′(t)=12t−4t2H''(t) = 12t - \dfrac{4}{t^2}H′′(t)=12t−t24 for t>0.5t > 0.5t>0.5, where t t\,t is the time in seconds after launch and H(t)H(t)H(t) is the height in metres.
At the instant t=1t = 1t=1, the height and vertical velocity of the drone are such that the tangent to the graph of H H\,H against t t\,t has the equation H=8t−5H = 8t - 5H=8t−5.
Find an equation of the normal to the graph of H H\,H at the point where t=1t = 1t=1.
Find H(t)H(t)H(t), writing your answer in simplest form.
864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.