3. A pilot is flying to a destination 230 km south of her current position. An air traffic controller tells her that the wind velocity (as seen on the ground) is 37 km/h [E25 °N]. She knows that the plane's speed is 281 km/h. a) Sketch the overall vectors of the plane to the ground, the plane to the air and the air to the ground. Write the equation for the velocity of the plane relative to the ground with the appropriate subscripts. b) Determine the heading of the plane (in what direction must the pilot fly to compensate for the wind?). Show your work. Label your vectors and label x and y components. c) How long will it take her to reach her destination if she goes at constant velocity with the heading you determined above? (Should it take longer or less time than with no wind?) d) How long would it take her to reach her destination if she went at constant velocity and there was no wind?

3. A pilot is flying to a destination 230 km south of her current position. An air traffic controller tells her that the wind velocity (as seen on the ground) is 37 km/h [E25 °N]. She knows that the plane's speed is 281 km/h. a) Sketch the overall vectors of the plane to the ground, the plane to the air and the air to the ground. Write the equation for the velocity of the plane relative to the ground with the appropriate subscripts. b) Determine the heading of the plane (in what direction must the pilot fly to compensate for the wind?). Show your work. Label your vectors and label x and y components. c) How long will it take her to reach her destination if she goes at constant velocity with the heading you determined above? (Should it take longer or less time than with no wind?) d) How long would it take her to reach her destination if she went at constant velocity and there was no wind?