Calculate the magnitude and direction of the resultant. Use drawings to illustrate.
1. A displacement of 12 km south followed by a displacement of 5 km east.
2. A velocity of 24 m/s north and a velocity of 7 m/s east.
3. A force of 12N west and a force of 16N south.
4. An aircraft, flying with an engine speed of 400km/h, is set on a course due north, at a wind speed of 60km/h from the southwest. At what speed and in what direction is the aircraft covering the ground?
5. A train is traveling 125 mph on a railway line that runs N 240 E and the direction of a canal is due east. Find the components parallel and perpendicular to the canal, of the velocity of the train.
6. A force of 100N is pressing vertically downwards on the inclined face of a wedge. If the angle of inclination of the wedge is 300, find the components of the force parallel to, and perpendicular to, the face of the wedge.