Finding Velocity of a ball hitting a ball hanging from a string

jheld

1. The problem statement, all variables and given/known data
A 20.0 ball is fired horizontally with initial speed Vi toward a 110 g ball that is hanging motionless from a 1.10 m -long string. The balls undergo a head-on, perfectly elastic collision, after which the 110 g ball swings out to a maximum angle theta = 50.0.

What was Vi?


2. Relevant equations

call ball mass .02 kg = A
call ball .11 kg = B
Avai + Bvbi = Avaf + Bvbf

Ki = Kf
(1/2)Avai^2 + (1/2)Bvbi^2 = (1/2)Avaf^2 + (1/2)Bvbf^2

vaf = (A - B)/(A + B) * vai


3. The attempt at a solution

vbi = 0 m/s
Bvbi = 0

Avai = -Avaf + Bvbf

vai = (A + B)/(A - B) * vaf

my problem is finding vaf, the final velocity of block A.

the final height y = L(1 - cos(theta)) = 1.1(1 - cos(50)) = .393 m

LowlyPion

You know the height the ball on the string went up to, so you know from conservation of energy and the m*g*h what the KE of the ball on the string was from the collision.

mv²/2 = m*g*h

jheld

Okay.

So, I find vbf = sqrt((2*g*h)), masses cancel out.
that gets me about 2.775 m/s

Vai = Vbf*(A + B)/2*A
which equals about 9.02 m/s.

and algebraically plugging it back in to find vbf, I find that my answer is correct (at least for the previous work that I did).
thanks