Show that the vectors a = 3i+ 4j and b = 4i - 3j are perpendicular. A smooth sphere A of mass 2m moving on a smooth horizontal floor with velocity (10i +5j)ms" impinges obliquely on a smooth stationary sphere B of mass m. At the instant of collision the line joining the centres of the spheres is parallel to the vectora. Given that the coefficient of restitution between the two spheres is e and that the direction of motion of sphere A afterimpact makes an angle a with the line of centres of the spheres, show that (a) (4-2e) tan a = 3, 3 (b) s tan a s- 2 (c) Given that tan a s1, find e and hence find the velocitics of A andB after impact.

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.