Suppose than an airplane starts at the point (x, y) = (a,0) located due east of...

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Suppose than an airplane starts at the point (x, y) = (a,0) located due east of its intended destination, which is an airport located at the origin (x, y) = (0,0). The plane travels with constant speed vo relative to the wind, which is blowing due north with constant speed w. (The direction of the wind is parallel to the y-axis, pointing upwards.) We assume that the plane's pilot, while in flight, maintains its heading directly toward the origin. (That is, after takeoff, the velocity has the same slope as the line going through the points (0,0) and (x, y), pointing toward the origin.) (a) Derive the plane's velocity components and . They will depend on vo and w. dt (b) Use them to obtain a differential equation in the form dy = f(x,y) for the trajectory y plane. (c) Show that the resulting equation is homogeneous and solve it. Then, determine y as a function of x. (d) Where will the plane be when x = 0 if wvo? g(x) of the Suppose than an airplane starts at the point (x, y) = (a,0) located due east of its intended destination, which is an airport located at the origin (x, y) = (0,0). The plane travels with constant speed vo relative to the wind, which is blowing due north with constant speed w. (The direction of the wind is parallel to the y-axis, pointing upwards.) We assume that the plane's pilot, while in flight, maintains its heading directly toward the origin. (That is, after takeoff, the velocity has the same slope as the line going through the points (0,0) and (x, y), pointing toward the origin.) (a) Derive the plane's velocity components and . They will depend on vo and w. dt (b) Use them to obtain a differential equation in the form dy = f(x,y) for the trajectory y plane. (c) Show that the resulting equation is homogeneous and solve it. Then, determine y as a function of x. (d) Where will the plane be when x = 0 if wvo? g(x) of the