Make an appropriate substitution

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Reference no: EM13218404

Differnetial Equations question

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D Aircraft Guidance in a crosswind

An aircraft flying under the guidence of nondirectional beacon (a fixed radio transmitter, abbreviated NDB) moves so that its longitudinal axis always points torward the beacon (see figure 3.19) A pilot sets torward an NBD from a point at which the wind is at right angles to the initial direction af the aircraft; the wind maintains this direction. Assume that the wind speed and the speed of the aircraft through the air (its "airspeed") remain constant. (Keep in mind that the latter is different from the aircraft's speed with respect to the ground.)

(a) Locate the flight in the xy-plane, placing the start of the trip at (2,0) and the destination at (0,0). Set up the differential equation describing the aircrafts path over the ground.
[Hint: dy/dx = (dy/dt)/(dx/dt).]

(b) Make an appropriate substitution and solve this equation. [Hint: See Section 2.6.]

(c) Use the fact that x = 2 and y = 0 at t = 0 to determine the appropriate value of the arbitrary constant in the solution set.

(d) Solve to get y explicitly in terms of x. Write your solution in terms of a hyperbolic function.

Reference no: EM13218404

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