23. (a)In the problem of the path of flight trajectories considered in class (p.21 notes) let 100miles and vo 40miles/hr. How far northward does the wind blow the airplane?W- (b) Suppose that an airplane maintains a heading toward an airport at the origin. If vo 500 mi/h and w 50 mi/h (with the wind blowing due north), and the plane begins at the point (200, 150), show that its trajectory is described by y V2 +20091/10 (c) A river 100ft wide is flowing north at w feet per second. A dog starts at (100,0) and swims at o4ft/s, also heading toward a tree at (0,0) on the west bank directly across form the dog's starting point. (a) If 2 ft/s, show that the dog reaches the tree. (b) If w 4 ft/s, show that the dog reaches instead the point on the west bank 50 ft north of the tree. (c) If w 6 ft/s, show that the dog never reaches the west bank.
