Two balls are moving on the same smooth horizontal plane. Their velocity components along one edge of a square plane are 10√3 m.s^-1 and 20 m.s^-1 respectively. Their velocity components along a perpendicular edge are 30 m.s^-1 and 20 m.s^-1. Find the angle between their directions of motion.

Taking ball 1, Velocity along let say x direction = 10√3 m.s^-1 Velocity along y direction = 30 m.s^-1  Resultant velocity is 20√3 m.s^-1 at an angle of 60 degrees with x direction (tan x = 30/10√3) x = 60 degrees Similarly for second ball resultant is = 20√2 m.s^-1 at an angle of 45 degrees. (tan x = 20/20 = 1) x =45 degrees So, the angle between their directions of motion is 60 - 45 = 15 degrees (Correct Answer)