I'YN.YMICS OF A POINT. 303 



and that the tension will be a maximum either at the 1 

 point of the tube, or at a point wluse projection on the axis 

 tance between the projections of the extremities. 



V. Resisting Me<lium, 



1 148. A heavy particle is projected vertically upwards, and 



(vol.)* 

 resistance of the air is m - ; x, y are the respective heights 



of two points in the ascent ami descent at which the particle 

 has the same velocity ; prove that 



1419. A heavy particle moves in a medium in which the re- 

 tries as the square of the velocity; v, v' are its velocities 



at the two points where its direction of motion makes an a: 

 with the horizon, and u the velocity at the hi-he.-t point; 

 that 



1 1 2 cos' 



A particle is moving under the action of gravity in a 

 medium whose resistance varies as the Minare of the velocity; 

 p t p a: : vutnre of its path at two points at each of 



which the direction of motion makes an angle a with the horizon, 

 f the radius of curvature at tin- ;><>mt; prove ti 



1. A small smooth bead slides on a fine wire whose \ 



of an\ point of which is asin , * 

 the arc measured from the lowest point, in a medium whose 



