Question

A 3.20-kg object is moving east at 4.50 m/s when it collides with a 6.00-kg object that is initially at rest. After the completely elastic collision, the larger object moves east at 3.13 m/s.

1) What is the final velocity of the smaller object after the collision? Assume that the positive direction is to the east.(Express your answer to three significant figures.)

Answer 1

The center of mass is traveling East at
3.20(4.50) + 6.00(0) = (3.20 + 6.00)v
v = 1.565 m/s

so from the COM, the 6.00 kg object appears to be moving

0 - 1.565 = -1.565 m/s
and after the collision, will appear to be moving the opposite direction at the same speed,
an observer on the ground would see that mass moving at the speed of the
COM plus the velocity of the departing mass relative to the COM.

1.565 + 1.565 = 3.13 m/s

Which agrees with our known result.

The COM sees the smaller mass moving in the positive direction at

4.5 - 1.565 = 2.935 m/s

and sees this mass depart at the same speed but in the opposite direction for a velocity of
v = - 2.935

a ground based observer would see the velocity of the COM plus the relative velocity of the smaller mass to the COM

v = 1.565 + (-2.935)
v = -1.37 m/s

as this value is negative, the smaller mass is moving west after the collision.