PRO 



city of projection, h height due to this velocity, a, = /.of projectioa 

 above the horizontal plane, i = elevation of the plane above the hori- 

 zon, g ~ 32 % feet ; then \ve have the following equations. 



A v * sin.8( <) _ , sin.* ( ) 

 ~ 2g ' cos. 3 ; cos. 2 > 



_ 2p sin. (-<) _ /2 A 2 sin. ( <) 



5- ' cosTT " g- ' cos. < 



Greatest range = 



2. When t = o; r will be the horizontal range, and the above equa- 

 tions will become 



r = . sin. 2 2 h sin. 2 . 

 A = -- . sin.2 = h sin. . 



t = . sin. = V ^- . 2 sin. . 

 # 



Greatest range = 2 A. 



3. The curve described by a projectile is a parabola, the principal pa- 

 rameter of which = 4 h cos. 2 , and the velocity at any point is that ac- 

 quired by falling from the directrix. 



4. To find an .equation to the curve, re- 

 ferred to horizontal and vertical co-ordi- s -n- 

 nates. 



Let AB = jr, B C = #, t = any time ; 

 then 



x v t cos. a. 



y = v t sin. <* and eliminating t. 



y x tan. --- 

 2 r* cos.* . ' 



the equation to the curve. 

 Cor. 1. If, as before, h = -~, 



