When there is an elastic collision, there conservation of momentum and kinetic energy. If the initial velocitie of the balls of masses m each are u and v and the final velocities after elastic collision are x and y, respectively, then the required equations are : mu+mv= mx+my for the conservation of momentum and mu^2+mv^2 = mx^2+my^2 for the consrvation of energy. Solving these equations, for x and y , i.e, the ball's respective velocities after impact, we get :
x = [(m-m)u +2mv ]/(m+m) and y = [2mu+(m-m)v]/(m+m)
Given that u=2 meter/s and v = 3 meter/s in opposite direction of u = -3 meter/s, and substituting to find the x and y the speed of the first and second balls, we get :
x=[(0+2m(-3)]/(m+m) = -3 meter per second and
y=[2m(2)+0](m+m) = 2 meter per second.
After the elastic collision, the first ball, which had its velocity +2m/s before impact, imparts its speed and direction also to the second ball and the second ball retraces back with a speed of 2m/s .
The second ball whose speed before impact was -3 meter per second imparts its speed and direction to the first ball and the first ball rebounds back with a speed , -3m/s as contrasted to its velocity of +2m/s before impact.
In other words, the balls exchanged their velocities after impact.
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