Question 6 - 12 marks This is a past examination question. A non-dimensional model of a glider flying to minimise flight-time in the absence of lift and drag is y' COS Y u' = - sin y E = ucosy , n = usiny where y is the flight-path angle, u is the non-dimensional velocity, & is the non-dimensional range, and n is the non-dimensional altitude and ' (prime) denotes differentiation with respect to 7, the non-dimensional time. The glider travels from $ = 0, n = ho to $ = L,n = h1, where ho > hi > 0, and, at the start of the motion, the glider is pointing vertically downwards so that y = -1/2. (a) Show that u = ccos y for some constant c 0 and hence show that dy/dr = 1/c. (2] (b) Find differential equations for d/dy and dn/dy. [2] (c) Find the general solutions of the differential equations in (b). 2 (d) Show that the flight-path is given by a cycloid. (e) How is the constant c determined? 2] (Hint for (d): let x = 5, y = ho - n and 0 = 1 + 27.)