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MATHEMATICS FOR AIR CREW TRAINEES 43-44

(5) A body is subjected to a force of 50 pounds acting toward 50° and a force of 70 pounds acting toward 340° at the same time. Find the direction and magnitude of a third force that will counterbalance exactly the effect of the first two.
(6) A man heads the bow of his boat directly across a river which is flowing at the rate of 2 mph. If he rows r mph, how much off his course is he at the end of 1 hour? How far does he go in 1 hour?
2 miles; √r^2+4 Answer.
(7) A man pushes on the handle of a lawn mower with a force of 75 pounds in line with the handle. The handle makes an angle of 30° with the horizontal. Find how much force is-
(a) Straight ahead.
(b) Into the ground.
44. Triangle of velocity.-a. The velocity of an object may be defined as a vector quantity the magnitude of which is the speed of the object and the direction of which is the direction of the object's motion. It can be represented by a directed line segment (vector). The velocity of a body which is acted upon by two forces can be found by considering the velocity resulting from each force individually. The actual, or total, velocity of the body is the resultant of the separate velocities. The velocity, relative to the ground, of an airplane in flight is the resultant of two velocity vectors: the air speed and heading vector, and the wind velocity vector. This resultant velocity vector is the course and ground speed vector.

[[image - three examples of using vectors to determine ground speed track vector]]
Figure 53.

b. The terms used are now defined as follows:
(1) Air speed.-The true speed of an aircraft relative to the air. Speed is given in mph or knots.
(2) True heading.-The angular direction of the longitudinal axis of the aircraft with respect to true north. The words "heading" and "true heading" will be used interchangeably.