Physics pls

a 4.0 kg mass is moving to the right at 3.0 m/s. an 8.0 kg mass is moving to the left at 2.0 m/s. if after collision the two masses join together, what is their velocity after collision?

-0.33 m/s
-0.20 m/s
+1.4 m/s
+2.3 m/s

-0.33m/s (A)

Explanation:

According to the law of conservation of momentum, the sum of momentum before collision is equal to sum of their momentum after collision. They move with the same velocity (v) after collision.

Momentum = mass × velocity

For 4kg mass with velocity of 3m/s,

Its momentum = 4×3 = 12kgm/s

For 8kg mass with velocity of 2m/s,

Its momentum = 8 × -2 = -16kgm/s.

The velocity of 8kg mass is negative because it is moving towards the left(-ve x-direction).

Sum of momentum before collision = 12+(-16) = -4kgm/s... (1)

Momentum of 4kg body after collision = 4v

Momentum of 8kg body after collision = 8v

Sum of momentum after collision = 4v+8v = 12v...(2)

Equating 1 and 2 according to law of conservation of momentum, we have;

-4 = 12v

V = -4/12

V = -0.33m/s

Therefore their velocity after collision is -0.33m/s