A non-dimensional model of a glider flying to minimise flight-time in the absence of lift and drag is COS Y u' = - sin y น " §' = u cosy, n' = usin y where is the flight-path angle, u is the non-dimensional velocity, & is the non-dimensional range, and ŋ is the non-dimensional altitude and ' (prime) denotes differentiation with respect to 7, the non-dimensional time. The glider travels from § = 0,ŋ = ho to { = L,n = h₁, where ho > h₁ > 0, and, at the start of the motion, the glider is pointing vertically downwards so that y = -π/2. |Show that u = ccosy for some constant c 0 and hence show that dy/dr = 1/c.

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