194 Dynamite. 



from which we deduce, 



sin a a = cos a a 

 or 



sin a* 



cos a* 

 , that is, 



trig. 8 



tang a 3 = 1, 

 and consequently, 



tang a = 1, 



in other words, the tangent of the angle of projection is in this 

 Tri 24 case ec l ua ^ to rac * ius j accordingly this angle is equal ' to 45. 

 Therefore, the greatest horizontal range is obtained, other things being 

 the same, when the angle, of projection is 45. It is here supposed 

 that 



Trig. 20. . - 



sin a = cos a = y/i ; 



this value substituted in the above expression for AC, gives 



therefore, J/ie greatest random is double the height through which a 

 body must fall to acquire the velocity of projection. 



307. If we would know to what height the body ascends, or 

 the highest point B of the curve, we proceed thus ; in the equa- 

 tion 



4 h y cos a 2 = 4 h x sin a cos a # 2 , 



we put equal to zero, the differential of */, taken by regarding x 

 only as variable, which gives 



4 h dx sin a cos a 2a?e?# = 0, 

 from which we obtain 



a? = 2 h sin a cos a ; 



2f)5 therefore, since AC = 4 fo sin a cos a, if we suppose the perpen- 

 dicular BD, we shall have 



x or AD = 2 ft sin a cos a = | 

 Moreover, this value of x being substituted in the equation, 



