( 2G9 ) 



DYNAMICS, ELEMENTARY. 



L Rectilinear nwtioti, Impulses. 



1286. A ball A impinges obliquely on another ball B y and 

 after impact the directions of motion of A and B make equal 

 angles 6 with -4's previous direction, find 6; and prove that when 

 A = B, = tan.~ l je, e being the mutual elasticity. 



1287. A smooth inelastic ball, mass m, is lying on a horizon- 

 tal table in contact with a vertical wall, and is struck by another 

 ball, mass m' 9 moving in a direction perpendicular to the wall and 

 inclined at an angle a to the common normal at the point of 

 impact ; prove that the angle 0, through which the direction of 

 motion of the striking ball is turned, is given by the equation 



7)1 



cot cot a = 1 + . 



M 



1288. Equal particles A lt A t , ... A m are fastened at equal 

 intervals a on a fine string, of length (n - 1) o, and are then 

 laid on a horizontal table at n const-cut ive angular points of a 

 regular polygon of p sides (/ n) each equal to a ; a blow P is 

 aj.j.lied to A } in direction A^A f ; prove that the impulsive ten- 

 sion of the string A r A r + t is 



(l+aina)*-(l-sina)* 



i * 2?r 

 a denoting , 



1289. Al\ PB are chords of a circle whoso diameter AB is 

 vertical; particles falling down AF, PB respectively, start 



