PROJECTILES 205 



FLIGHT OF PROJECTILES 



166. By a projectile here is meant any body which is small 

 enough to be regarded as a particle, and which is projected in such 

 a way that it describes a path under the influence of gravity. 



A projectile will, in general, be influenced by the resistance of 

 the air as well as by gravity, but we shall suppose the resistance 

 of the air to be negligible, so that gravity will be the only force 

 which need be taken into account. 



To take the simplest case first, let us imagine that the projectile 

 is projected horizontally from the point (fig. 116), with velocity u. 

 The only force acting is gravity, which o 

 has no horizontal component, so that 

 the horizontal velocity remains equal to 

 u throughout the motion. The initial 

 vertical component of velocity is nil, 

 but there is a downward acceleration g. 

 Thus after time t, the horizontal dis- 



tance described is ut, while the vertical 



i o -r^ FIG. 116 



distance fallen is \gt. Denoting the 



horizontal distance described by x, and the vertical distance fallen 

 by y, we have x = uf 



The equation of the path described is obtained by eliminating t 

 from these equations, and it is found to be 



2 u* 

 This is a parabola, of which the latus rectum is -- 



9 



Clearly the problem of determining the curve is essentially the same as 

 in 156. There we have a body falling freely, and tracing its path on a 

 paper which moves post it with a uniform horizontal velocity. Here we have 

 a body falling freely, and can imagine it to trace its path on a paper past 

 which it moves with a uniform horizontal velocity. The relative motion is 

 the same in the two cases, so that the curves are necessarily the same. 



