A text book of elementary mechanics, for the use of colleges and schools . Fig. 22. cal line FAB is a diameter. The constant value of the is four times the distance from A ratio of BC2 2ri A B \ 9 to the directrix or to the focus. The same relation is at 49.] PEOJECTILES. 45 once obyious in the case of the parabola, whose equationis if = iax ( —- = ia); it may also be proved analyti-cally for this case, where the co-ordinates EB, AD arcoblique. It is proved geometrically in a following para-graph (50, e). If AE is taken on the vertical line equal to —, and EGE be drawn horizontally, this l
A text book of elementary mechanics, for the use of colleges and schools . Fig. 22. cal line FAB is a diameter. The constant value of the is four times the distance from A ratio of BC2 2ri A B \ 9 to the directrix or to the focus. The same relation is at 49.] PEOJECTILES. 45 once obyious in the case of the parabola, whose equationis if = iax ( —- = ia); it may also be proved analyti-cally for this case, where the co-ordinates EB, AD arcoblique. It is proved geometrically in a following para-graph (50, e). If AE is taken on the vertical line equal to —, and EGE be drawn horizontally, this line will be the direc-trix; and if from A on the line AF (drawn so that the , u2angle EAD = DAF) we take AF = —, the point i^is the focus of the parabola. The vertical line GML isthe axis. If the direction of the initial velocity be horizontal, asin Fig. 23, then the starting-point ^A is the vertex, the vertical line AB *is the axis, .and the focus and direc- ?* 2? 2?. Fig. 23. trix are at distances equal to — from A. This figure shows well, as doesalso Fig. 21, what is meant by thestatement in (27), that in uniformly #».,accelerated motion the space is pro-portional to the square of the time. Here, if the suc-cessive intervals of time are equal, AD : AD : AD : AD, etc., = 1:2:3:4,and AB : AB : AB : AB, etc., = 1 : 4 : 9 : 16. 49. The actual path of a projectile deviates widelyfrom a parabola because of the resistance of the air,which is very great with high velocities, as that of acannon-ball or rifle-bullet (perhaps 1600 feet per second 46 KINEMATICS. [50. in starting). For this reason the maximum distance isgained, not by an angle of 45° (as shown below), but foran angle of a little over 30°. A jet of water illustrates the subject of the projectilewell, since each particle may be considered as an inde-pendent projectile, and thus the shape of the jet giyesthe continuous path. It shows, moreover, the deviationcaused by the resistance of the a
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectmechanics, bookyear18
