MOTION of BODIES, with their Velocities. 1. If the quantities of matter in any two or more bodies put in motion, be equal, the forces wherewith they are moved will be in proportion to their velocities. 2. If the velocities of these bodies be equal, their forces will be directly as the quantities of matter contained in them. 3. If both the quantities of matter and the velocities be unequal, the forces with which the bodies are moved will be in a proportion, compounded of the quantities of matter they contain, and of the velocities wherewith they move. E. 51. There are two bodies, the one contains 25 times the matter of the other (or 25 times heavier) but the leffer moves with 100 times the fwiftnefs of the greater; in what proportion are the forces by which they are moved ? As 35 : 100 I I 25)100(4 100 Anf. 4, the lefs is moved with a force fo much greater than the other. E. 52. There are two bodies, the greater contains 9 times the quantity of the matter in the lefs, and is moved with a force 48 times grea ter; the ratio of the velocity of these two bodies is required? Anf. Leffer than the greater as 1 to 51. Note, In comparing the motion of bodies, if their velocities be equal, the fpaces defcribed by them are in direct proportion of the times in which they are described. 2. If the times be equal, then the spaces defcribed will be as their velocities. 3. If the times and the velocities be unequal, the fpaces will be in a proportion compounded of the times and velocities. E. 53. There are two bodies, one of which moves 80 times fwifter than the other, but the fwifter body has moved but one minute, whereas the other has been in motion two hours: the ratio of the spaces defcribed by these two bodies is required? First 2 hours X 60 120 minutes; then E. 54. A may-pole 50 feet 11 inches long, at a certain time of day cafts a fhadow 98 feet 6 inches long; I would thereby find the breadth of a river, that running due E. and W. within 20 feet 6 inches of the foot of a steeple 300 feet 8 inches high, which throws the extremity of its fhadow 30 feet 9 inches beyond the stream? In figure 5, Fb = 50 feet 11 inches, 611 inches, the height of the may-pole; and Db 98 feet 6 inches, or 1182 inches, length of its fhadow. Alfo BC= 300 feet 8 inches, or 3608 inches, the height of the fteeple; and AB the length of its fhadow; then: E. 57. St. Martin's spire in Birmingham, at a certain time projected upon level ground, a fhadow to the distance of 144 yards, 2 feet, z inches, when my cane, 3 feet 2 inches in length, perpendicularly erected, caft a fhadow of 6 feet 3 inches; from hence the height of the fpire is required? FIGURE 6. E. 58. There are two bodies, one whereof has defcribed 50 miles, the other only 5, but the firft has moved with 5 times the velocity of the fecond; what is the ratio then of the times they have been describing thofe fpaces? First, 50-5-10; then: I 5)10 Answer 2 So that the first body hath been in motion double the time of the fecond. XIII. RECIPROCAL PROPORTION: OR, THE RULE OF THREE INVERSE. RECIPROCAL PROPORTION is, when of four numbers, the third beareth the fame proportion to the firft, as the fecond doth to the fourth; confequently, the lefs the third term is in respect to the first, the greater will the fourth term be in refpect to the fecond. RULE. Multiply the first and fecond terms together, and divide their products by the third term, the quotient will be the answer required. Therefore, it is only varying the operations, and you have a proof to all questions of this nature, |