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. 1892 Excerpt: ... path. NOTE. This proposition may be stated as follows; When any particle has fallen vertically under the action of gravity from a point on the directrix to a point on the parabola, it has a vertical velocity downwards, whose magnitude is equal to the velocity which the particle describing the parabola has when at that ...
Read More
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. 1892 Excerpt: ... path. NOTE. This proposition may be stated as follows; When any particle has fallen vertically under the action of gravity from a point on the directrix to a point on the parabola, it has a vertical velocity downwards, whose magnitude is equal to the velocity which the particle describing the parabola has when at that point. It must be noticed that these two velocities are not in the same direction. It follows that the horizontal speed is that due to falling from the directrix to the vertex, and hence that the number of feet in the i1fi cos2ct latus-rectum of the parabola is----. 128. Another proof of Art. 127 is as follows. Let the tangent at P cut the axis of the parabola in T. The vertical velocity at A is zero; so that the vertical velocity at P(usma) is that due to falling a vertical distance AN; hence asin2a = 2g AN. Now in the parabola with the usual notation iAN= NT= PTsin a = 2/-Ksin a = i5/sinao, whence 2 sin2 0 = igSP sin2 a, or U% = 2gSP. Q. E.D. Example i. To find the range and time of flight on an Inclined plane, angle a, which passes through the point of projection. Resolve the velocity of projection along and perpendicular to the inclined plane; the resolutes of the velocity are, in velos, initially, cos(0-a); sin(0-a); after t secs, cos (0-a)-(g sin a) t; u sin (6-a)-(gcos a) t. The resolutes of the displacement for / secs, in the same directions are in ft., t secs., u cos (0-a) t-J (sin o) t; u sin (0-a) t-(gcos a) P. The particle strikes the plane again when the displacement perpendicular to the plane, viz. sin (9-a)t-$ (gcos o) fl, is zero;. 2 sin I0-a) that 1s, when t = 5. cos a Let 00" in the figure be the range; draw 0"M perpendicular to the horizontal line 00; then 0M= hori...
Read Less
Add this copy of Elementary Dynamics: Being a New and Enlarged Edition to cart. $50.84, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2011 by Nabu Press.
