Synopsis
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. 1828 Excerpt: ...inclined to their direction at an angle of 45. Given the distance at which one impinges upon the other on the horizontal plane, and the point from which one of them descended, to find the point from which the other began its motion. 60. In the case of the preceding problem, shew that if a circle be described passing through the two points from which the balls began their motion, and touching the horizontal plane, the point of contact will bisect the distance between the vertical line and the point where they impinge on each other. 61. On a given straight line perpendicular to the horizon, as diameter, describe a circle, and draw a tangent at its higher extremity. Then if from any point in this tangent a straight line be drawn parallel to the diameter, cutting the circle in two points, from which horizontal chords are drawn; the times of falling down the parts of this line, together with the times of describing the corresponding chords with the velocities acquired at their extremities, are equal. 62. If a body be projected obliquely upwards, shew that the square of its velocity will always be equal to the square of the velocity of projection, diminished by the square of the velocity which it would acquire by falling down its perpendicular height above the horizontal plane passing through the point of projection. 63. If a body fall («) feet the last second; determine the height fallen from, supposing the force of gravity to vary inversely as the square of the distance. 64. Compare the space described in 1" by the force of gravity in any given latitude, with that which would be described in the same time if the earth did not revolve round its axis. 65. Let two bodies move with known uniform velocities in given directions AP, BQ: determine when their ...
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