136 
MOTION OF A PROJECTILE 
and if B be the value of X when x = %K> then 
and 
2 s — 5 s = 35 s 
X ? 
£ 3 ' 
If A be the value of X when x — a, then 
l_i 3 = 3^; 
or 
73 & 
3 A* + ii 3 ’ 
and 
4 — 45 3 4^ 3 
~ 46 3 - 1 — IP - A* 
When z = 1, p =- orco; consequently, when x = a, the tangent 
CL 
is at right angles to the tangent at the origin, and when x = 4 K — a, 
the tangent is the vertical asymptote. Therefore the distance of the 
vertical asymptote from the origin is 
w 3 3* (4 K — a) 
g (4 4- « 3 )« (4 + 4« 3 )^ ° 
There will be another vertical asymptote, corresponding to x = — a, 
to the trajectory described when the velocity at the origin is reversed. 
(The figure is drawn for a = fJf. A is the point where the tangent is perpendicular to the 
tangent at the origin, and then x = f K; J3 and JB' are the points where the velocity is a minimum, 
and then x = ± §K. For OB, x = pT; for OB', x = - f K.) 
