The outlines of physics: an elementary text-book . ath is pararbolic. As before, y^, y^, y^, y^ are the successive positionswhich would be reached in 1, 2, 3, and 4 seconds, un- GRAVITATION 33 der gravitation alone. The positions Vj, v^, v^, v^ corre-spond to a;^, x^, 3:3, x^ of Example 1. They are the posi-tions which would be reached were no forces to modifythe motion of p. The po-sitions actually reached are PV P2 is Vi- 32. Example 3. (Initialvelocity vertical.) — Thereare two cases; of upwardand of downward initialvelocity, respectively, butboth are solved by the sim-ple numerical process
The outlines of physics: an elementary text-book . ath is pararbolic. As before, y^, y^, y^, y^ are the successive positionswhich would be reached in 1, 2, 3, and 4 seconds, un- GRAVITATION 33 der gravitation alone. The positions Vj, v^, v^, v^ corre-spond to a;^, x^, 3:3, x^ of Example 1. They are the posi-tions which would be reached were no forces to modifythe motion of p. The po-sitions actually reached are PV P2 is Vi- 32. Example 3. (Initialvelocity vertical.) — Thereare two cases; of upwardand of downward initialvelocity, respectively, butboth are solved by the sim-ple numerical process ofcomputing the positionwhich would have beenoccupied had gravitationnot acted, and the positionin case the initial velocityhad been zero. These are subtractedwhen the initial velocityis upwards, and addedwhen it is downwards. Given an upward initialvelocity of 1000 cm. persecond: to find the posi-tion of the projectile after3 seconds (g = 980). Without gravitation itsposition would be 3000 the starting point. Gravitation, but for the. Fig. 24, 34 THE OUTLINES OF PHYSICS initial velocity, would carry it downwards over a path s,such that 980 X 9 or «= ? 4410. 2 Pg, the new position, is 4410 — 3000 = 1410 cm. belowthe starting point. Had the initial velocity been 1000 cm. downward thenew position would have been found at 4410 + 3000 =7410 cm. below the starting point. 33. The Ballistic Curve. — Thus far we have consideredprojectiles moving under a single constant force. Inreality, however, projectiles are subjeeted to other forces,such as the ordinary resistance of the atmosphere and theforce of the wind. These modify the path of the projec-tile and cause it to deviate from the parabolic form. Inthe case of projectiles of high speed this divergence, isconsiderable, and it has to be taken accurate accountof in the science of gunnery. Along parabolic paths, forexample, in order to carry a shot to the greatest distance,the elevation of the gun must be 45° above the
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