What Is the Final Velocity of the Larger Ball After Collision?

[felipenavarro]

Homework Statement

a small ball of mass "m" is traveling with an initial velocity v in the positive x direction. it collides with a larger vall of mass M that is initially at rest. after the collision, the smaller ball is at rest. What is the final velocity, V, of the larger ball?

options are:

a. V=v
b. V=-v
c. V=0
d. V=(M/m)v
e. V=(m/M)v

Homework Equations

The Attempt at a Solution

well, i understand that in order for a ball to have a velocity of 0 after colliding(in a elastic collision) with another one, the other one must have equal mass and it will continue with the velocity the first one had. in the problem it says that the second one has greater mass so it can not be an elastic collison because the firs ball would have bounced off with a negative velicocity. so it must be inelastic and if they are stuck together both have a speed of 0.

ok, this is one way of looking at the problem but i don't know if it is correct.

answer e also looks correct because it is what you get after solving momenun initial=momentum final

which one is correct?

 

[SHISHKABOB]

use conservation of momentum, what is the result?

 

[felipenavarro]

with conservation of momentum it is answer e. but isn't the reasoning i said before correct?

 

[SHISHKABOB]

imagine a bowling ball and a tennis ball floating in a vacuum or something

isn't it possible to hit the bowling ball with the tennis ball and the result be that the tennis ball ends up with zero velocity and the bowling ball moves a little? It's a very precise situation.

 

[felipenavarro]

your right,! i didnt thought about a low speed.

 

[SHISHKABOB]

you can see that the final velocity of the larger mass is going to be some smaller fraction of the smaller guy's initial velocity because it's v(m/M)

m/M is always going to be some fraction less than one

only when the smaller mass ends with a velocity of zero, ofc