Elements of Mechanics; Treated by Means of the Differential and Integral Calculus

Elements of Mechanics; Treated by Means of the Differential and Integral Calculus

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1859 edition. Excerpt: ...we shall have, y=Q.... (120.) To find the point at which the trajectory will reach any horizontal plane B C, whose distance below the point A is h', we make y = /t', in-(120), whence, ... (121.) On account of the resistance of the air, the results of the preceding discussion will be greatly modified. They will, however, approach more nearly to the observed phenomena, as the velocity is diminished and the density of the projectile increased. The atmospheric resistance increases as the square of the velocity, and as the cross section of the projectile exposed to the action of the resistance. In the air, it is found that, under ordinary circumstances, the maximum range is obtained by an angle of projection not far from 34. EX A MPLE S. 1. What is the time of flight of a projectile, when the angle of projection is 45, and the range 6000 feet? Solution. When the angle of projection is 45, the range is equal to twice the height due to the velocity of projection. Denoting this velocity by w, we shall have, e = 2ffh = 2 X 321 X 3000 = 193000. Whence, we find, v--439.3 ft. From Equation (117), we have, r 6000. t =-=----= 19,3 sec. Ant. vcosa, 439.3 cos45 2. What is the range of a projectile, when the angle of projection is 30, and the initial velocity 200 feet? Ans. 1076.9ft. 3. The angle of projection under which a shell is thrown is 32, and the range 3250 feet. What is the time of flight? Ans. 11.25 sec., nearly. 4. Find the angle of projection and velocity of projection of a shell, so that its trajectory shall pass through two points, the co-ordinates of the first being x = 1700 ft., y--10 ft., and of the second, x--1800 ft., y = 10 ft. SOLUTION. Substituting for x and y, in Equation (115), (1700, 10), and (1800, 10), we have, Finding the value...show more

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  • Paperback | 92 pages
  • 189 x 246 x 5mm | 181g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236581830
  • 9781236581839