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bigred
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This is a differential equations problem that I've been having some trouble with. A plane is flying and always pointing towards point (0,0) on an xy plane. Wind is constantly blowing North (positive y direction). The wind speed and speed of the aircraft through the air are constant.
(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 a differential equation describing the aircrafts path over the ground.
(b) Make an appropriate substitution and solve this equation.
(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.
(e) Let gamma be the ratio of windspeed to airspeed. Using a software package, graph solutions for the cases gamma = 0.1, 0.3, 0.5 and 0.7 all on the same set of axes. Interpret these graphs.
(f) Discuss the (terrifying!) cases gamma = 1 and gamma greater then 1.
My attempts to find a solution to this word problem are pretty pathetic. Any help would be appreciated.
(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 a differential equation describing the aircrafts path over the ground.
(b) Make an appropriate substitution and solve this equation.
(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.
(e) Let gamma be the ratio of windspeed to airspeed. Using a software package, graph solutions for the cases gamma = 0.1, 0.3, 0.5 and 0.7 all on the same set of axes. Interpret these graphs.
(f) Discuss the (terrifying!) cases gamma = 1 and gamma greater then 1.
My attempts to find a solution to this word problem are pretty pathetic. Any help would be appreciated.