50 OUTLINES OF NATURAL PHILOSOPHY. 



projected,) the directrix of the parabola described 

 by the projectile is a horizontal line drawn through 

 that point, in the plane of the projection ; and the 

 velocity of the projectile in every point of its path, 

 will be the same that it would have acquired by 

 falling freely from the height of the directrix. 



a. All the parabolas described by bodies projected 

 from the same point, and with the same velocities, 

 though with different elevations, have the same di- 

 rectrix ; and have their foci in the circumference of 

 the same circle. 



95. If a body be projected with the velocity c 9 

 and in a direction that makes an angle E with the 

 horizon, the distance at which it will strike the ho- 

 rizontal plane, (or what is called its horizontal 

 range), will be equal to twice the perpendicular 

 height to which it would be carried by its initial 

 velocity, multiplied into the sine of double the 



angle E ; or = sin 2 E. 



o 



a. Hence the greatest horizontal range is, when the 

 direction of the projectile makes an angle of 45 

 with the horizon : Also with respect to every other 

 range, there are two angles which will give the same 

 range, the one as much less than 45 as the other is 

 greater. 



2 96. The 



