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 (x, y). 



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

 direction making an angle a with the axis sc. 



Fig. 30. 



We have the equations sc = 0, 



2/ = -#&amp;gt; 

 with the conditions that when t = 0, 



sb = 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. 



