1. A plane takes off from an airport which is at sea level. The aircraft's altitude in metres at a time of t minutes is modelled by the equation h = 5400 In(t + 1) a) What is the height of the plane after five minutes? b) What is the rate of climb of the plane after five minutes? c) Using differentiation, show the curve y = h(t) has no stationary points, and hence comment on how realistic the model would be for large t.2. A particle moves in a straight line and, at time t, has velocity v ms'1 with u = int 129' (t 2 0) a) Find an expression for the acceleration of the particle at time t. b) When t = 0, the particle is at the origin. Write an expression for the displacement ofthe particle at time t. 3. The distance, x mm, moved by a particle is related to the time in seconds. We have x = 1.2 sin(2t) Find the distance travelled, the velocity and the acceleration of the particle at a time of t = 0.3 seconds.4. The velocity, v ms-1, of a fairground ride t seconds after it begins is given by v = (3e-t + 7)sint What is the acceleration of the ride 2 seconds after it begins?5. What is the area enclosed by the graph of y=x2+x2 below the x-axis? 5. A window is in the shape of a semi-circle over a rectangle, as shown. The distance around the outside of the window is 12 metres. What dimensions will result in the rectangular portion of the window having the largest possible area