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" If a body acted upon by gravity be projected in a medium the resistance of which varies as the square of the velocity... "
New series of The mathematical repository - Page 21
by Thomas Leybourn - 1835
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University of Cambridge, Sir Thomas Gery Cullum - 1830
...attractive or repulsive force, the tension at any point is inversely as the perpendicular from the center of force upon the tangent at that point. 8. Find the...the square of the velocity, find the equation to the carve described ; and when the resistance vanishes, shew that it is the equation to a parabola. TUESDAY...
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Problems in the different branches of philosophy: adapted to the course of ...

Miles Bland - Trigonometry - 1830 - 374 pages
...moving in directions making equal angles with the horizon, then will t 2 "* = 1 + 2ns'. 85. If a body be projected in a medium, the resistance of which varies as the velocity, and be acted on by gravity ; and another be projected in vacuo, at the same angle, and with...
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Dynamics, Or an Elementary Treatise on Motion: With a Great Varity of ...

Samuel Earnshaw - Attractions - 1832 - 185 pages
.../?, v = 0, 197. To determine the motion of a body descending in a circular arc, acted on by gravity in a medium, the resistance of which varies as the square of the velocity. Using the notation of Art. 113, and putting v for the velocity at P, we have the accelerating force...
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Mathematical problems and examples, arranged according to subjects, from the ...

Mathematics - 1836
...upon its circumference ; find the velocity of the chain at the end of a given time. 118. If a body be projected in a medium, the resistance of which varies as the velocity, and be acted on by gravity, and another be projected in vacua at the same angle, and with...
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A collection of problems in illustration of the principles of theoretical ...

William Walton - Science - 1842 - 451 pages
...differential equation to the curve in x and r. Euler; Mechan, torn. п. р. 246. (4) To find the tautochrone in a medium the resistance of which varies as the square of the velocity, the particle being acted on by gravity. Let 0 (fig. 150) be the point to which the particle is always...
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Dynamics: or, A treatise on motion; to which is added a short treatise on ...

Samuel Earnshaw - Attractions - 1844 - 372 pages
...the velocity of the body. Hence the ultimate value of PT is . 302. A heavy body descends from rest in a medium, the resistance of which varies as the square of the velocity, toJlnd the space described in a given time. Let a be the space descended in the time t ; \/~kdfs Vg...
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A collection of problems in illustration of the principles of theoretical ...

William Walton - Science - 1847 - 230 pages
...— 437. 4. To find the centre of resistance on a semicircular plate, revolving about its diameter in a medium, the resistance of which varies as the square of the velocity. Let ft> denote the angular velocity of revolution, a the radius of the circle, x the distance of the...
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University of Cambridge, Sir Thomas Gery Cullum - 1849
...the motion of a material particle which falls from rest under the action of a constant force, through a medium the resistance of which varies as the square of the velocity. Shew that the velocity of the particle never exceeds a certain limiting value, to which it approximates...
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A Treatise on Infinitesimal Calculus: Containing Differential and ..., Volume 3

Bartholomew Price - Calculus - 1856
...particle projected with a given velocity in a line inclined at a given angle to the horizon, and moving in a medium the resistance of which varies as the square of the velocity. In this case the equations of motion are, as in Art. 302, dx _ ,dsdx ~w = ~ dtdi (70) rf**~ dt dt If...
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A treatise on the dynamics of a particle, by P.G. Tait and W.J. Steele

Peter Guthrie Tait, William John Steele - 1865
...moves being uniform, and the resistance varying as the square of the velocity. (10) If one particle be projected in a medium, the resistance of which varies as the velocity, and be acted on by a constant force parallel to a given line, and another be projected in...
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