Aball has a mass of 0.25 kg and is moving to the right at 1.0 m/s. it hits a ball of mass 0.15 kg that is initially at rest. after the collision, the 0.15 kg ball moves off to the right with a velocity of 0.75 m/s. what is the final velocity of the 0.25 kg ball?

Hello!!

So we have a conservation of momentum problem here.

we are told we have .25kg ball with velocity of 1.0m/s. It collided with .15kg ball with initial velocity of zero and ending velocity is .75m/s

p=mv is momentum. So in this case we find each balls momentum and find the difference then set that momentum value equal to the first ball * v1f and solve for the final velocity of the first ball(v1f). So we have

p1=.25kg*1.0m/s = .25(kg*m/s) so now we find second ball momentum.

p2=.15kg*.75m/s= .113kg*m/s

so now we find the change in momentum is .25-.113=.137

So we have

.137kg*m/s=.25kg*v1f so final velocity of first ball is

v1f=.137/.25= 0.55m/s in the positive x direction.

Hope this helps you understand the concept Thank you so much!!

0.55 m/s to the right is the answer.