Answer
(a) The speed of ball 1 in this reference frame is 0.
The speed of ball 2 in this reference frame is $9~m/s$ and the ball is moving to the left.
(b) The speed of ball 1 in this reference frame is $9~m/s$ and the ball is moving to the right.
The speed of ball 2 in this reference frame is 0.
Work Step by Step
(a) If the reference frame moves with ball 1, then the speed of ball 1 in this reference frame is 0.
We can find the speed of ball 2 in this reference frame:
$v_{2,1} = v_2-v_1$
$v_{2,1} = (-3~m/s)-(6~m/s)$
$v_{2,1} = -9~m/s$
The speed of ball 2 in this reference frame is $9~m/s$ and the ball is moving to the left.
(b) If the reference frame moves with ball 2, then the speed of ball 2 in this reference frame is 0.
We can find the speed of ball 1 in this reference frame:
$v_{1,2} = v_1-v_2$
$v_{1,2} = (6~m/s)-(-3~m/s)$
$v_{1,2} = 9~m/s$
The speed of ball 1 in this reference frame is $9~m/s$ and the ball is moving to the right.
