260 
PRINCIPLES OF GUNNERY. 
Integrating again. 
x == Vt cos a, . 
y = Vt sin a — Igfi ; 
.( 1 ) 
.( 2 ) 
Equation or, eliminating l between equations (1) and (2), 
jectory. 
o 
CJX“ 
y = x tan a — J 
2 V 3 cos 3 a 5 .* 
wbicli is the equation of the trajectory of an unresisted projectile. 
( 3 ) 
Elementary The same results may be obtained more simply by considering the 
S slon conditions of motion. Thus, suppose [x,y] the co-ordinates of the 
conditions 
of motion. 
1 
M- 
t 
V P 1 
-i 
P 
0 
N < 
projectile (P) at time t. Then 
• 
3 
ON=x, 
NP=y , 
horizontal velocity at muzzle = V cos a 
and since there is no resistance, and gravity acts only in a vertical 
direction, 
the horizontal velocity at any point in the trajectory is the same, and equal to V cos a. 
Again, 
vertical velocity at muzzle = V sin a. 
This vertical velocity is diminished by gravity acting vertically 
downwards— i.e., by gt in time i —so that 
vertical velocity at any time, t, is equal to V sin a — gt. 
V 
The horizontal velocity being constant, and equal to V cos a, it 
follows that 
the horizontal distance {ON) traversed by the projectile in time t 
— V cos a X t 
or x s± Vi cos a„ 
a) 
