A 6 kg ball moving west at 4 m/s collides with a 4 kg ball moving east at 3 m/s. What is the velocity (magnitude and direction) of the 4 kg ball after the collision if after the collision the 6 kg ball comes to a stop?

This is a conservation of momentum problem. We know the momentum initial=momentum final.

Momentum = mass * velocity

Ball 1 has a mass of 6kg and initial velocity of 4and final velocity of 0

Ball 2 has a mass of 4 and a initial velocity of - 3 and a final velocity of x

Notice i set west as postive velocity and east as negative.

Momentum initial = ball 1 momentum (inital) + ball 2 momentum initial.

= 6kg * 4 m/s + 4kg*-3m/s = 12kgm/s

Momentum final = 6kg*0m/s + 4kg*x

Since final = inital

12 = 4x

X=3 m/s

Since it is positive that means 3 m/s west