Question

A billiard ball with a mass of 4 g is moving east while a second ball...

A billiard ball with a mass of 4 g is moving east while a second ball with a mass of 3 g moves west. Positive x axis is due east. The two balls come into head on collision while moving in their respective velocities. Assume that the motion is one dimensional and the collision is perfectly elastic. If the initial velocities of the balls are 12 cm/s and 10 cm/s, what are the velocities of each ball after the collision?

m1 = 4 g

u1 = 12 cm/s

m2 = 3 g

u2 = 10 cm/s

Using conservation of momentum we can write

--------------- (1)

and using conservation of energy we can write

or

--------------- (2)

Using equation 1 and 2

v2 = 15.143 cm/s or -10 cm /s and

v1 = -6.857 cm /s or 12 cm/s

So velocity of 4 g mass is 6.857 cm/s toward West and velocity of 3 g mass is 15.143 cm/s toward East

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