Physics Problem: Calculating Velocity of a Thrown Ball at State Fair Booth

[sweetpea1993]

ok here the question:
jamal is at the state fair playing some of the games. at one booth he throws a 0.50-kg ball forward woth a velocity of 21.0 m/s in order to hit a 0.20-kg bottle sitting on a shelf, and when he makes contact the bottle goes flying forward at 30-0 m/s.

A) What is the velocity of the ball after it hits the bottle?

 

[dacruick]

so we assume its an elastic collision. which means momentum and energy are conserved. but since you have the end speed of the bottle we won't need energy.

so we know that the intial momentum of the bottle is 0, and the initial momentum of the ball is (0.5)*(21)

we know that the final momentum of the bottle is (0.2)*(30) and the mass of the ball stays the same.

so that means that (0.5)*(21) = (0.2)*(30) + (0.5) * (final speed of ball)

 

[sweetpea1993]

so does that mean the answer would be 9?
(0.5)(21)=(0.2)(30)+(0.5)(x)
10.5=6+(0-5)(x)
x=9??