Projectiles

(pro-jektilz.) [From L. project us, thrown to a distance.] (Mech.) When a body is thrown vertitically upwards it moves in a straight line, and returns to the place from which it started. When, however, the direction of projection makes an angle with the vertical, the body describes a curve. Suppose the direction of projection-to be horizontal; in order to find the position of the body at any time, we must apply the second law of motion. Now, the force of gravity will draw it as far from the horizontal line of projection in agi ven time when it starts with a certain velocity, as when it starts from rest. If, therefore, we mark off on a horizontal line the positions which the body would occupy at succe ive intervals of time if gravity did not act upon it, and from each of these points draw a vertical line equal to the space through which a body would fall freely up to the instant marked by the points, and join the extremities of all the lines thus drawn, we obtain the path of the projectile. This construction is precisely that required to draw the curve called in geometry a parabola. Hence, if the resistance of the air be not taken into account, the path of a projectile is a parabola. To determine the greatest height to which a projectile will rise, the velocity at starting is resolved into two components, one vertical, the other horizontal, and the greatest height is found by dividing the square of the vertical velocity by twice the acceleration of gravity. The range on a horizontal plane is found by dividing twice the product of the vertical and horizontal velocities by the acceleration of gravity. The range of a projectile will be greatest when the angle of projection is 45°. In this theory the resistance of the air has not been taken into account, and this resistance affects the motion so materially as to render the parabolic theory nearly usele in practice. The path inclines to the earth more rapidly than is the case with a parabola, hence the range is much le . For example, when the velocity is about 2,000 feet, the resistance of the air is 100 times the weight of the ball, and the greatest range, which, according to theory, should be 23 miles, is le than 1 mile. [s. 734]