An approach path for an aircraft landing is shown is the figure and satisfied th

Question

An approach path for an aircraft landing is shown is the figure and satisfied the following condition: The crushing altitude is h when descent starts at a horizontal distance t from touchdown at the origin The pilot must maintain a constant horizontal speed v throughout descent. The absolute value of the vertical acceleration should not exceed a constant k (which is mush less than the acceleration due to gravity). Find a cubic polynomial P(x) = ax2 + bx2 + d that satisfies condition by imposing suitable condition on p(x) and p'(x) at the start of descent and at touchdown. Use conditions and to show that Suppose that an airline decides not to allow vertical) acceleration of a plane to exceed k = 860mi/hr2. If the cruising altitude of a plane is 35.000 ft and the speed U 300 mi/hr, how far away from the a upon should the pilot start descent? Graph the approach path if the conditions stated in Part c) are satisfied.

Explanation / Answer

i) P(x) = ax^3 + bx^2 + cx + d P'(x) = 3ax^2 + 2bx + c P(x) passes through, (0,0). This gives 0 = a*0 + b*0 + c*0 + d So, d = 0. Also, P'(x) at (0,0) is 0. Therefore, 0 = 3a*0 + 2b*0 + c So, c = 0. P(x) passes through (l,h). This gives, h = al^3 + bl^2.......................(1) Also, P'(x) at (l,h) is 0. So, 0 = 3a*l^2 + 2b*l........................(2) Solving (1) and (2), a = -2h/l^3, b = 3h/l^2 Thus, P(x) = -2h(x/l)^3 + 3h(x/l)^2

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