44 MOTION IN TERMS OF ACCELERATION. [CHAP. IV. 



body. The acceleration of a free falling body at a place is known 

 as the acceleration due to gravity at the place. Its magnitude 

 depends upon the latitude of the place, in London it is about 981 '8 

 when the centimetre is the unit of length, and 32'2 when the 

 foot is the unit of length, the unit of time in both cases being 

 the mean solar second. The letter g is commonly used to denote 

 this acceleration. 



45. Parabolic motion. Let the velocity of a particle at 

 time t be parallel to the plane of (x, y), and let its acceleration 

 be uniform and parallel to the negative direction of the axis of 

 y. Take g to be the measure of the acceleration. 



Since the acceleration parallel to the axis z is always zero, the 

 particle does not acquire velocity parallel to this axis ; and, since 

 at time t = it has no velocity parallel to this axis, it undergoes 

 no displacement parallel to this axis ; thus the point moves in a 

 plane parallel to the plane (#, y). 



At time t = suppose the velocity of the particle is V in a 

 direction making an angle a with the axis x. 



Fig. 30. 



We have the equations x = 0, 



y = -0, 

 with the conditions that when t 0, 



x = V cos a, y = V sin a. 

 Since x = 0, we have x = V cos a always. 

 Since y = -g, we have y = V sin a - gt after an interval t. 



