Question

A 10.0 g object moving to the right at 15.0 cm/s makes an elastic head-on collision with a 15.0 g object moving in the opposite direction at 33.0 cm/s. Find the velocity of each object after the collision.

10.0g object _________

15.0g object _________

Answer 1

Given m = 10 g

         M = 15 g

Initial velocities u = 15 cm / s

                       U = -33 cm / s

Here negative sign indicates that both u and U are opposite in direction.

Coefficient of restitution for eleastic collision e = 1

     i.e., relative velocity after collision / relative velocity before collision = 1

               V - v / ( u - U ) = 1

                             V - v = u - U

                                    = 15 -( -33)

                                    = 15 + 33

                                    = 48

                                V = v + 48            -----------( 1)

From law of conservation of linear momentum ,

mu + MU = mv + MV

(10x15) +(15 x -33) = 10 v + 15 ( v+48 )        Since from equation(1)

150 - 495 = 10 v + 15 v + 720

-345 = 25 v + 720

                     25 v = -345 -720

                            = -1065

                         v = -42.6 cm / s

From equation ( 1) , V = v + 48

                                 = -42.6 + 48

                                 = 5.4 cm/s