88 



KINEMATICS. 



[167. 



Taking the horizontal line through the starting point O as 

 axis of x, the vertical upwards as positive axis of y (Fig. 42), the 



x 



Fig. 42. 



^-component of the acceleration is evidently o, while the jj/-com- 

 ponent is g\ hence, by (4), Art. 160, the equations of motion 

 are 



S =o> = -^- (4> 



The first integration gives 



dx _ dy_ 



As -^=z/ z , -ssy t are the components of the velocity v at 

 at at 



the time /, the constants are determined from the values of v m v v 

 at the time /=o; viz. V Q cos 6=^, V Q sin e = o -f- C z . We have 

 therefore 





(5) 



^ z = = V Q cos e, v y = - = VQ sin e gt. 



Integrating again, we find 



X=V Q cos e t, y ^Q sin e t \gfi, (6) 



the constants of integration being o, since for t=o we have 



These values of x, y, v x , v y show that the motion in the hori- 

 zontal direction is uniform while in the vertical direction it is 



